You should have asked your boyfriend about his interactions with this other woman. Then, if he told you that nothing was going on, you would have to take his word for it. Otherwise, you lose trust in your relationship. If he told you that he was interested in this other woman, you could simply break up with him and move on.
You should have never confronted the other woman. That was a waste of time AND it made you look unstable. Also, she, more than likely, has designs on him and this outburst of yours played right into her hands. You practically chased him away and into her arms.
You were not wrong to be suspicious, but as I stated before, you are in a relationship that REQUIRES trust in order to last. In these situations, you always have to simply trust until you have proof. It is the risk we take when we give out heart away.