Trust is broken.. Don't know what to do

So i have been dating my bf for about two months now. We lived in different cities. We talked for about 3 month before we started dating. Recently, I did a traditional dance for the Lunar New Year, and i met some girls from the dance. My bf also came with me to rehearsal sometimes. He's a friendly guy, so he talks to them. One of the girls asked him for his snapchat id and they started snapchating. They became friends on fb and have been talking. I'm pretty sure my bf is the one that started the conversation... so then they exchanged numbers and they keep texting and snapchatting each other everyday from morning to night. I know this because he was still texting and snapchatting her when he's next to me, when he came visit me. She's also in a relationship. One day, I went to work and he and my other guy friend and her hung out. My guy friend went home after about 2 hours and my bf hung out with her for the whole day. She's in cosmetology so he asked her to cut his hair, she took him to a restaurant to eat before she dropped him off at my apt. 

I got upset, and i told him that i don't like that he keeps talking to her everyday. They just met, what do they have so much to talk about? He told me that they're just talking as friends, but i told him that feelings grow. He said that he won't do that again, that he won't text her again, but the next day, he did it again behind my back. When his phone beeped, he won't check it when I'm there, he only does it when i'm not in the room. I told him that night that i knew that he was still texting and snapchatting her behind my back. He said he knew, and he just wanted to see how I react and how long I can hold it. I got really mad and told him that he knew how i would react. After that, he just does it right in front of my face, not hiding anymore although he already promised that he wouldn't do it again. I told him that it makes me feel unwanted when he does that and it still didn't get to him. My sister talked to him when i wasn't there and he told my sister that "jealousy is such an eyesore" She told him that so is inconsiderate. I asked him to put himself in my shoes. How would he feels if i do the same thing to him with another guy and I was very disappointed in his answer. All he said was go ahead and do it because he trusts me. We have been in this relationship for 2 months. I don't think our trust bond is strong enough for him to say that. I started losing trust in him. He told me that he asked the girl if her bf is ok with them talking and she said her bf is fine with it. I didn't believe him when he said that. I told him that i don't feel secure in our relationship that i'm losing trust and all he said was to trust him, and that he's not gonna cheat on me.

I needed security and he wasn't giving me it. I texted the girl and asked her. She said that they're just talking as friends and she wouldn't do anything out of line. I believed her. I told her to put herself in my shoes, what would she feel if her bf is hanging out with her but talking, laughing with another girl on the phone. She said she understands and she would stop talking to him if i want her to. I told her that it's not that i don't want them to be friends, it's just that they are doing it too excessively. It was too much. My bf also accused me for having a friend look at his phone. I told him that I would never ever, in a million year do that. He said: "Well, your friend didn't act on his own, did he?" I got really hurt when he said that. He said he trusted me but he's not believing in what I'm telling him. When we have calmed down, I told him that it made me really sad when he said that and he doesn't know me at all. I'm not that kind of person. We decided that we're gonna wait to see if the girl is gonna text him first. I told him that if the situation get too uncomfortable for me and if it doesn't get any better, i'm going to remove myself from the situation. It got so bad that i got traumatized by his ringtone, when it rings, i keep thinking it was her, although i know i shouldn't think that, and it's probably not her all the time. 

My sister was texting me and we were talking about the situation. She said that he's not a man and that he's not good enough for me. She also asked me if i wanted some space. I said yes.. I don't have a password on my phone. So, the next day, while I was taking a shower, he looked at my phone and at my messages with my sister. He saw it and got upset.. He didn't wanna talk to me and ignoring me. I knew right away that he looked at my phone. I asked him but he denied. He was mad at me and he went to text her although we agreed that we were gonna wait. I was really hurt, and i felt like he was really immature for doing that. I talked to him and i told him how that made me feel and he said he was sorry. I also told him that he said he trust me but he looked through my phone, that's not trust. He apologized for hurting my feeling and he said he sees where i'm coming from. I told him that i was trying to build that trust with him, but when he texted her behind my back after he told me he wouldn't and when he looked through my phone, and texted her when he was mad at me, he knocked down my trust again and again. He went home and he said that he hasn't texted her for a couple days and asked if i trust him. Honestly, i didn't know if i trusted him or not. I told him that i will not bring it up again and let's forget it. 

He came to visit again last weekend and I know that he was texting her and snapchatting her again too. Idk who started and i know he was doing it less though. Idk if the girl doesn't answer all the time or is it him who was stopping. so i don't know if he was telling the truth when he said he stopped texting her for a couple days when he was at home. I don't really know what to do now. He sometimes make jokes about it. One of his friends knows about the situation so he was joking, saying let's go eat at "the girl's name" house. And my bf said, I can ask her... then he laughs. When i was joking that I'm gonna leave him and his friend to walk home, he said I know who to ask for a ride. then laughs. He knows that it makes me uncomfortable but why does he keep saying things like that. I keep telling myself that it's nothing because he likes to make friends, but at the same time, i can't help my feeling. I feel like he's still snapchatting her and texting her. I just want some opinion on the situation. What do soompiers think? Am i being too much? I just don't know what to think anymore. Our relationship is so new, and i already lost trust in him.