He Doesn't Trust Me Despite All I've Done.

Good day ma, I have been in a relationship for a year and some months, the guy is in UK. We talk all the time through phone, though we started the relationship before he travelled. The problem now is that he doesn't trust me despite all said and done.
He has my Facebook password, he will go and search for some of my message of five years ago, and he will call me and start calling me names.
Sometime ago, he accused me of sleeping with my brother's friend, I got angry and decided to end the relationship. The worst he did now is, I chatted an old friend on Facebook, he called me, and start saying that am a prostitute. I can't imagine a man I want to spend the rest of my life with calling me names now.
Am confused, I don't know if I should continue with him or I should just hope on God for another relationship, I feel I went too for giving him my Facebook password etc


There are three major ways men discharge a lady who they're no longer interested in dating. (Read»»Three Major Ways Men Break-up with a lady).  

Immediately he travelled to UK, his dating value rose and he became an international single man who have the privilege to toast any Nigerian lady and she'll be experiencing orgasm in her dreams. He now has the opportunity to date Nigerians in UK and of course other ladies who are non Nigerians. 
And you see, your undying love is irritating him which is why he's using the messages that Facebook themselves sent to you against you so that you will then give up and leave him. That way it will be assumed that you decided to leave and not the other way round. 
Since it's obvious that he's no longer interested in dating you, I will suggest that you consider moving on with your life and learn from this experience. 
Whenever a man makes you feel inferior, it's obvious that he's not emotionally mature for a long term relationship. Again, dating a partner who doesn't trust you or believe in your personality is as good as wasting your time and emotions building what will never stand the test of time. 
So there's no need to panic, simply make it easier for him, change your password and move on with your life. You deserve a better partner than one who makes you feel less of a lady.