Ruling on taking birth control pills before the farewell tawaaf

Firstly: 

Tawaaf al-ifaadah is one of the pillars or
essential parts of the Hajj, which is not waived in the case of a
menstruating woman or anyone else, but the menstruating woman cannot
circumambulate the Ka‘bah until she becomes pure (i.e., her period ends and
she does ghusl), because the Prophet (blessings and peace of Allah be upon
him) said to ‘Aa’ishah when she menstruated: “Do what the pilgrims do,
except do not circumambulate the Ka‘bah until you become pure.” Narrated by
al-Bukhaari (1650) 

It says in al-Mawsoo‘ah al-Fiqhiyyah
(18/320): There is no difference of opinion among the fuqaha’ that menses
does not prevent the woman from doing any of the actions of Hajj apart from
tawaaf, because the Prophet (blessings and peace of Allah be upon him) said
to ‘Aa’ishah when she menstruated: “Do what the pilgrims do, except do not
circumambulate the Ka‘bah. End quote. 

There is nothing wrong with a woman taking
some medicine to prevent menstruation or shorten its duration, so that she
will be able to circumambulate the Ka‘bah (tawaaf). 

Shaykh ‘Abd al-‘Azeez ibn Baaz (may Allah
have mercy on him) was asked:

 What is the ruling on a woman using pills
to prevent her monthly period during the days of Hajj? 

He (may Allah have mercy on him) replied:
There is nothing wrong with that, because it serves a purpose, so that she
will be able to do tawaaf with the people and so that she will not hold her
travelling companions back.

End quote from Fataawa Islamiyyah
(2/185) 

For more information, please see the
answer to question no.
112271 and

36600

Secondly: 

With regard to the farewell tawaaf, an
exception was made for menstruating women. al-Bukhaari (1755) and Muslim
(1328) narrated that Ibn ‘Abbaas (may Allah be pleased with him) said: The
people were commanded that the last thing they should do is to
circumambulate the House, but an exception was made for menstruating women. 

Ahmad (3495) narrated that Ibn ‘Abbaas
(may Allah be pleased with him) used to say that the Prophet (blessings and
peace of Allah be upon him) granted a concession allowing the menstruating
woman to leave before doing tawaaf, if she had already done tawaaf al-ifaadah. 

It says in al-Mawsoo‘ah al-Fiqhiyyah
(18/320): The fuqaha’ are unanimously agreed that the menstruating woman may
leave (Makkah) without doing the farewell tawaaf, so as to make things
easier for her, because of the hadeeth of ‘Aa’ishah (may Allah be pleased
with her), according to which Safiyyah (may Allah be pleased with her) got
her menses, so the Prophet (blessings and peace of Allah be upon him)
instructed her to leave without doing the farewell tawaaf. And it was
narrated that Tawoos said: I was with Ibn ‘Abbaas when Zayd ibn Thaabit
said: You issue fatwas stating that the menstruating woman may leave without
the last thing she does being to circumambulate the Ka‘bah. Ibn ‘Abbaas said
to him: Why not? Ask So and So the Ansaari woman whether the Messenger of
Allah (blessings and peace of Allah be upon him) instructed her to do that.
Then Zayd ibn Thaabit came back to Ibn ‘Abbaas smiling and saying: I see
that you are right. End quote. 

As that is the case, so long as there will
be no harm done by your continuing to take those pills until you have
completed all the rituals of Hajj and done the farewell tawaaf around the
Ka‘bah, that is good, especially when the time between the two tawaafs is
usually short. 

But if you fear that this may cause you
harm, then there is nothing wrong with you refraining from it. If you remain
pure (i.e., do not get your period), then that is fine, otherwise you may
avail yourself of the concession granted by the Messenger of Allah
(blessings and peace of Allah be upon him) to the menstruating woman, by
leaving without doing the farewell tawaaf. 

And Allah knows best.