Trust is lost, is it time to end it?

I was with the girl im currently hooking up with yesterday lol, and she needed to make copies while we were on my way back to my house, keep in mind that she has told me previously that she doesnt trust me fully, I said why is that? she said "I just dont" so ultimately where we left off at is, me saying "I understand that, and I cant make you feel any different about the situation all I can tell you is that its going to make things difficult if you dont trust me, and she agreed, I told her that Im not asking her to trust me fully as I feel like thats something that shes gotta decide upon. So anyways we were getting out the car and I left my phone in there, I guess I received a text when she was getting out, and she had the audacity to grab my phone and check who was texting me, it turned out to be one of my friends who is a girl asking me what I was gonna do tonight and if I wanted to meet up with her. Initially i believe that cell phones are someones personal space, I also believe that if you go looking for something, your sure to conjure up something in your mind to make it more than it is, it always goes back on trust. and I told her I dont appreciate you going through my phone as I dont go through yours and I think thats personal space, and she was pissed so she stayed silent, as for the text I explained to her that its a friend and she might as well have a penis because shes one of the homies haha. Later on she said that she has to meet every girl that I have as a friend before I hang out with them. I explained to her that, thats a ridiculous request and I dont feel thats necessary, she also said that I have 24 hours to change my relationship status on facebook haha or she breaking it off, which I just laughed at and told her that if she wants to say things like that then she can keep it moving anyway haha. I told her that I believe a relationship is between 2 people and essentially the world doesnt need to be included, as long as we understand what we have theres no need to include anyone on what we have. I just feel like I deserve to be happy and that I deserve to be trusted by someone that I care about, I dont think that this relationship is ideal for me simply because theres no trust and if theres no trust then theres no relationship