He has become Muslim but his mother wants him to go back to being a Christian

Firstly: 

We congratulate you for this blessing that Allaah has
bestowed upon you, for by Allaah it is the greatest of blessings and it is
guidance by means of which we ask Allaah to admit you to Paradise and join
you thereby with the Prophets, siddeeqs, martyrs and righteous.
Congratulations to you, for you have turned to Allaah at the same age at
which many of the best of the companions of the Prophet (peace and
blessings of Allaah be upon him) turned to Him, such as Mus’ab ibn ‘Umayr,
‘Abd-Allaah ibn Mas’ood, Mu’aadh ibn Jabal and Sa’d ibn Mu’aadh.
Congratulations, for the record of your deeds has become white and pure,
uncontaminated with sin. Islam erases that which came before it, so now you
are starting a new life, a happy life in sha Allaah. We ask Allaah to
protect you, make your heart steadfast and guide your parents, siblings and
loved ones. 

Secondly: 

We praise Allaah that you have started the path of guidance
by going to the mosque and studying the Qur’aan, for this is a good sign.
The Prophet (peace and blessings of Allaah be upon him) said: “When
Allaah wills good for a person, He grants him understanding of Islam.”
Narrated by al-Bukhaari, 71; Muslim, 1037. You should do your utmost to
memorize Qur’aan and recite it, pray at night (qiyaam), learn its rulings
and act upon it, because in Paradise there are different degrees and levels,
and it will be said to the companion of the Qur’aan in Paradise: “Recite and
rise (in degree), for your status will be commensurate with the last verse
you recite.” 

Thirdly: 

The attitude that your mother is expressing towards you comes
as no surprise. Your real battle is with the shaytaan, who is not pleased
that you have become Muslim, and he does not wish you well. Undoubtedly he
will make use of your relatives and whisper to your family, so that he can
use them as a weapon against you and prevent them from joining you in the
true faith. Do not grieve or despair; seek refuge with Allaah from the
accursed shaytaan so that his plot against you may be foiled. Be kind and
compassionate towards your mother, for if she tasted the sweetness of
guidance, she would not stand in your way. Seek the help of Allaah in
calling her to Islam, be sincere towards her and make a great deal of du’aa’
for her, asking for guidance and mercy for her. Perhaps your du’aa’ will
coincide with a time when prayers are answered, and you will have the joy of
seeing her become Muslim. 

Remember that you are not alone in this matter. There are
thousands of people whom Allaah has guided to the truth and who have chosen
Islam willingly, out of conviction. Many of them have met with opposition
and resistance from their families, then Allaah willed that their hearts
should be opened, and the entire family has become Muslim. That will weigh
in the balance of the son who was first guided. We ask Allaah to make you
one of them and to grant you the joy of seeing your whole family become
Muslim. 

Remember that opposition from family members is a test for
the Muslim, so that the sincerity of his Islam and the strength of his faith
may be made manifest. Allaah says (interpretation of the meaning): 

“Alif‑Laam‑Meem.

[These letters are one of the miracles of the Qur’aan, and
none but Allaah (Alone) knows their meanings.]

2. Do people think that they will be left alone because
they say: “We believe,” and will not be tested.

3. And We indeed tested those who were before them. And
Allaah will certainly make (it) known (the truth of) those who are true, and
will certainly make (it) known (the falsehood of) those who are liars,
(although Allaah knows all that before putting them to test)”

[al-‘Ankaboot 29:1-3]

Among these examples of righteous believers is the great
Sahaabi Sa’d ibn Abi Waqqaas (may Allaah be pleased with him) who used to
honour his mother. When he became Muslim, his mother refused to eat or drink
until he recanted his faith, but he refused to do so and remained steadfast
in Islam. His mother found no benefit in her “hunger strike” so she went
back to eating and drinking. It is narrated that he (may Allaah be pleased
with him) said: “O mother, you know by Allaah that if you had one hundred
souls and each soul departed one by one, I would not give up this religion
of mine for anything. If you wish, then eat, and if you wish, then do not
eat.” So she ate. 

See: Tafseer Ibn Katheer, 3/429 

Fourthly: 

The Qur’aan also deals
with this problem, because it happened a great deal, especially in the first
generation that left kufr behind and embraced Islam, and experienced intense
hostility from their family, tribe and the closest of people to them. Allaah
says (interpretation of the meaning): 

“And We have enjoined on
man (to be dutiful and good) to his parents. His mother bore him in weakness
and hardship upon weakness and hardship, and his weaning is in two years –
give thanks to Me and to your parents. Unto Me is the final destination.

15. But if they (both) strive with you to make you join in
worship with Me others that of which you have no knowledge, then obey them
not; but behave with them in the world kindly, and follow the path of him
who turns to Me in repentance and in obedience. Then to Me will be your
return, and I shall tell you what you used to do”

[Luqmaan 31:14-15]

There is no room for obeying parents in kufr, or for obeying
them in sin, but this does not mean that one should not treat them with
kindness and respect, and take care of them, and do one’s utmost to guide
them. This is indicative of the greatness of Islam, for it is the religion
of compassion and love. Hence it calls upon its followers to guide people
and bring them into the blessing into which they have entered. 

Fifthly: 

The one who has chosen the path of guidance should not pay
any attention to what other people say and he should not be surprised by it,
because that is something to be expected. What else will the Christians say
about you? Will they say, “You have been guided and found the truth and you
show it preference over your family and relatives”? No, they will never say
that! So do not pay any attention to what they say, whether they call you a
traitor or anything else. Regard them with compassion and strive to guide
them, and strive to learn so that you can become a daa’iyah who can save
them from their misguidance and deviation. 

With regard to your mother’s saying that you are inferior
because you were born Christian, this is not true. Rather we say that you
are our brother; you have chosen guidance and have returned to the fitrah
(natural state of man) in which you were born. You were born a Muslim and a
believer in Tawheed. The Christian scholars know that the child is born in a
state of fitrah, hence they hasten to baptize the infant, believing that if
he is not baptized he will become a Muslim! This indicates that the basic
nature of man is Islam, and that if the child were left as he is he would be
a Muslim.  

In Islam, no one is inferior to anyone else, except to
Muhammad (peace and blessings of Allaah be upon him), because the
Prophet is the Messenger whom we are commanded to follow. Apart from that,
Islam teaches its followers to be free from the domination of priests,
rabbis and monks, and states that a person has no need for any intermediary
between him and Allaah. 

Finally, you say in your question that your girlfriend has
accepted that you are Muslim and that you are planning to get married in the
future. Here it should be noted that because Islam is keen for its followers
to be chaste and for their hearts to be pure, it forbids men to have
girlfriends. Islam does not approve of any such relationship between a man
and a woman unless it be within the framework of marriage. If your
girlfriend is a Christian, then you have to call her to Islam and strive to
guide her. This will bring a great deal of good for both of you, in sha
Allaah. If she refuses then tell her that Islam forbids this relationship
between you and that you can never put pleasing anyone, no matter who he or
she is, before pleasing the Most Merciful. You should either get married
(and it is permissible for a Muslim man to marry a Christian woman) or
separate, preferring to seek the pleasure of Allaah, may He be glorified and
exalted. 

The most important advice we can give you is to treat your
mother and father, siblings and relatives, kindly and understand their
feelings. Ask Allaah to guide them, and choose wise methods of calling them
to Islam, such as kind words, gifts, visits, inviting them to visit the
mosque, and giving them useful booklets and tapes. 

We ask Allaah to take care of you and to help you to do all
that is good. 

And Allaah knows best.