Should I Let Him Go...?

I already know that I'm going to get judged for this so I'm not going to ask for no judgement here

Me and my boyfriend have been together for about 2 months, he's 20 and I'm 18. A little while ago, he caught me lying about something, and accused me of cheating. No, I've never cheated on him, or even thought about cheating because this is my first real relationship, and I wouldn't mess this up for anything. We are sexually active ourselves, but I only see him about once every week or every other week. Anyways, he said he is having a hard time trusting me, after I lied to him (i lied about the reason for putting condoms in my purse; the ones we had gotten from PPH at the time. I kept some because we usually forget to buy some, and then we would have to stop before we had sex to go get some, so when we went to PPH for my BC, I asked for some. When he asked me why I put some in my purse, it caught me so off guard that I lied and said it was because he liked the red ones, which was a total lie because he asked me that before we even tried any of them. And he caught that lie and he accused me of cheating). So fast forward a little bit: I went up to the mountains with my family Saturday night for a BBQ/Bonfire, and I couldn't tell him I was up there because there wasn't any service up there, so when I got home (we left around 6pm and for back at around midnight) he was a little upset because I didn't tell him I was going, and he didn't say it directly, but I could tell he thought I was out doing something else. So yesterday, he completely ignored my texts ( texting is how we usually communicate) and finally last night he just said he was having a hard time trusting me.

I know I lied. It was stupid to lie in the first place because I'm not good at it anyways. But I've been thinking a lot about our relationship(as most girls/women do when in a situation with a SO), and maybe it would be best if we just ended it.

I feel like it would be better for him if we did, because I feel like he doesn't think of me the same way anymore, or that he isn't happy anymore, but I don't want to end it just because things got hard and I could probably earn his trust back.

He was the first person I had sex with, and we did kind of jump into a lot intimate things so fast, but I don't regret any of it.

What should I do? Call it off, for his sake, because maybe it would be best? Or work it out, because this is just a bump in the road and we could totally work it through?

What are some ways I could earn his trust back, even though we don't see each other that often?

Thank you girls

- Ash (:

PS: And I know I might get some hateful comments, because I deserve it for lying. I get that..