Having trouble trusting my boyfriend
So about 2-3 weeks ago my boyfriend and I broke up for like 4 days. In those four days he started talking to this other girl who is friends with my younger sister. We got back together though so I assumed they stopped talking. Until yesterday, I noticed that she was his snapchat best friend and him and I snapchat a lot so they would have to be talking quite a bit for her to get to be his number one best friend. So I immediately assumed they were flirting because that's how they started back when we were broken up. In my moment of anger I tweeted "idk if you know the difference between single and taken but taken means DONT F***ING TOUCH HIM U T**T".
My sister questioned me about it so of course I told her because she's my sister. This his she went straight to her friend and told her what I said. Which made her message my boyfriend. She asked him if we were still together and he replied with "I don't know" when he's been telling me that we are 100% back together. My sister showed me the messages. So I asked him about that and he said it was easier than saying yes. I don't know what that means? So I decided I wanted to know if he was saying stuff back to her. I got my sister to text her and ask. She replied by saying she didn't want to intrude anymore. That obviously meant something. So I went to my boyfriend in person. I asked him if he was flirting back with her and he said "not going to lie I was a little bit" my heart literally broke.
This isn't like him at all, we've been together for almost 6 months and so far he's been perfect. I don't know why he did this. He apologized and told me it wasn't right of him to do that. I asked if he wanted to be with her and he said he only want me and that he's sorry and he didn't mean anything by it. I told him that I still wanted to be with him too. So we are still together however I still have this sinking feeling. I'm still very upset but I don't want to break up with him, maybe if he had done this before I would but no. I just don't know if I can trust him.
How do I know he's not going to do this again? I just feel so embarrassed because all his friends knew and I hang out with them sometimes. I feel humiliated basically and I don't think he gets that. I just don't know how to move on.. (We are both 16)