Hi & welcome Confused Guy
I'm a bit confused myself.
You really like this girl, yet while she's with you, sleeping, you send 'hey sexy' texts to other girls, making her angry & upset, because she now can't trust you.
She, meanwhile, receives 'have sex with me' texts from other boys & you are not sure that you believe that they are just friends.
You say that this girl cares about you; you kiss and hold hands & she stays at your frat house, but you are also just friends.
It seems, to me, that you need to sort out just exactly what your relationship is. It seems that you are more than just friends, but that one or both of you is / are unable or unwilling to commit to a real relationship.
Whatever the relationship, you need to rebuild the trust. It will be easier to do so, if there are no doubts, or unknowns, which may result in jealousy, etc. Perhaps you should have a serious chat about how things really stand between you.
Getting drunk won't help if you are trying to sort things out and avoid making 'stupid decisions'.
Good luck
