Does this mean that it's over between us?

Two nights ago I was in my boyfriends car and we were having a good time then all of a sudden I saw him texting someone and her name had the couples iPhone emoji (the one with the couple kissing) saved next to it (the same way my name is also saved). I instantly started ignoring him and got an attitude and just left the car to go back home because I didn't want to instantly jump into conclusions. Then when I got back home I called him and he forwarded my call and texted me saying that I should bug off and I shouldn't call him. I then replied by asking who the girl is and I called him then he said that I have an attitude, he doesn't like my attitude so I should call him tomorrow because he's talking to someone (must have been the girl I saw on his phone). Then I got angry and started saying that I'll leave him alone for good because I can do what he is doing too. I didn't call him after that and we're both stubborn so I know that he wouldn't call me, am I the one in the wrong here?

Neither of you are in the right - you overreacted and he acted "mannish" at your first spying on him, then distrusting him, and then calling him out. So while both of you need to get your pipes cleaned out being stubborn is the least of your problems.

It sound like both of you need some new turf. Not only are you both "stubborn" (as you put it) but - far more importantly - you don't trust each other and no relationship can last long without trust.

You should learn from this. Think twice before making accusations or saying things you might regret in the future. And chose your friends carefully so you can be confident in them.