Need an outsider opinion

I'm 19, my boyfriend is 21. We have been dating for about 3 years ago. A few months ago we got into an argument and he told me some stuff that happened during our first few months of dating. Basically, him lying about where we went and some text messages I saw that I thought were inappropriate. Since then I haven't really been able to trust him, I want too. But I'm not sure how too. As I continue through university I feel as if I haven't been given the opportunity to explore being with other people or doing anything out of the ordinary. Such as studying abroad or going on a vacation with some girlfriends. I don't wanna break up with him. But at the same time I do want to explore the world as a young adult. 
Any thoughts or advice?