Asalamualaikum sister
Woahhh, complicated situation, hmmmm, well first of all don't marry your cousin, thats a life long commitment, taht just sounds like a trainwreck ready to commence. I think you should talk to your university and talk about the situation that your in, and they may possibly help you with accomidation etc. So im assuming your family knows your a lesbian? So in Islam, homosexuality isn't permitted, and im not going to go off on a tagent and be ignorant or what not, but i think the root of the problem, is your family having a problem with your sexuality. So you should discuss that firstly (which is going to be difficult) and explain your side, but reassuring them that you love them, and never in any means meant to hurt them etc