So this girl I really like has a boyfriend. And I don't know whether to go after her or just let her be.?

Iam sorry to say this but just let her be, nowadays a lot of *** hole guys want to fight when someone gets in the middle of a relationship so if you dont like fights then just stand back even though that sucks. I have been there numerous times. who knows she may end up single again but dont put your life on hold for that. best of luck