I feel as if I'm wading into quicksand here, but what the heck...
If the girl assumed that she would be free to see somebody else and you didn't, you have a problem with communication. It is up to you whether you want to break up, live with the situation or tell her to stop seeing the other boyfriend. If you choose the third way, be prepared to split up - she might say forget it.
If the girl said that she would see only you, then she has lied and you have a problem with trust, which is very hard to fix. Again, it is up to you as to how to go ahead.
One thing you must NOT do is start seeing another girl just to get revenge. It will be bad for everybody, but especially for the other girl. She will end up feeling awful.
There are no definite answers here, as the details are not clear (and I don't want them to be.) I'm merely mentioning possibilities.