I did not let my husband read a message from my friend, and he got angry

May Allah bless you for hastening to apologise to your friend, for this is
indicative of your good character. 

I
ask Allah to relieve your distress and reconcile between you and your
husband. 

I
also offer you the following advice: 

Firstly: 

Undoubtedly the husband has confirmed rights over his wife, so she is
enjoined to obey him, treat him well and give precedence to obeying him over
everything else. Allah, may He be exalted, says (interpretation of the
meaning):

“Men are the protectors and maintainers of women, because
Allah has made one of them to excel the other, and because they spend (to
support them) from their means”

[an-Nisa’ 4:34]. 

It
was narrated that Abu Hurayrah (may Allah be pleased with him) said: The
Prophet (blessings and peace of Allah be upon him) said: “If a woman offers
her five daily prayers, fasts her month (Ramadan), guards her chastity and
obeys her husband, it will be said to her: Enter Paradise by whichever of
the gates of Paradise you wish.”

Narrated by Ahmad (1661); classed as saheeh by al-Albaani in Saheeh al-Jaami‘
(660) 

Secondly: 

The husband has no right to enquire into his wife’s private matters or her
correspondence or phone conversations with her female friends, so long as
everything is normal, praise be to Allah, and there is no cause for doubt or
suspicion. 

But the fact is that you asked him for advice when your problem with your
friend first began, which led to him asking to see the message, according to
what you mentioned in your question; he would not have asked to see that
message if you had not asked him for advice. Your refusing to show him the
message was not appropriate, especially since you were the one who asked him
for advice. Moreover he is your husband and he has rights over you. 

What you should do now is be kind to him and treat him nicely, and calm his
anger with nice words and good treatment. If you know that if he sees this
message, it will calm him down and put an end to this matter, then there is
no reason why you should not do that. In fact we advise you to let him see
it, even if that is contrary to the basic principle (and proper etiquette)
and even if that is part of your private matters. The interest of
reconciling between you and resolving the crisis takes precedence over
protecting this privacy. 

Seek reward with Allah for that and seek refuge with Him, so that you may
protect your family and your marriage. 

 Thirdly: 

The problem is minor, in sha Allah, and it is not wise or reasonable – or
even prescribed in Islam – to let such minor problems lead to turning the
home upside down, as you say, or reaching a dead end. 

Take care of your household and your family, and be patient with your
husband, for this is a storm that will pass quickly, in sha Allah; it is a
temporary misunderstanding that will soon end by the grace of Allah. 

Be
smart and wise in your interactions with him, and do not tell him about your
problems with your friends again, so that this problem will not be
repeated. 

We
ask Allah to reconcile between you and to restore your life to normal. 

And Allah knows best.