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

Praise be to Allah.

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.