Regardless of whether you want to stay in a relationship with her or not she has a problem.
Cutting herself is not normal thing to do. If you care at all for her or her welfare try and get her some help for this problem.
It is a difficult situation and you should not feel pressured to stay...
How long have you had the fish? They only live up to 2 years and it sounds like old age. Have had many Betta's and they do go through their last weeks as if having some mystery disease.
