Am I wrong for reacting this way?

The other day I was at my boyfriend's house and while we were watching a movie, I got bored and reached for his phone. His phone was locked, but while I was scrolling down his messages, I came across a text message that another female sent him referring to him as "babe". I got upset and asked him who it was, he then told me that it was his cousin and she was in another country. I'm not the kind of spouse that requires the passwords to their SO cellphone, social media accounts and etc. So when I seen the message, I got upset because I trusted him. I then told him that I was done with the relationship. I'm 18 y/o & he's 25 y/o, and we recently started dating. I don't really have much experience with dating, so I'm not sure if I overeacted or if my reaction was justifiable. Am I right for reacting this way or did I overreact?
Am I wrong for reacting this way?
5
13
Add Opinion