you don't have to cut yourself off from her to feel better about it.
it may be a constant thorn in your side, that's true, but you can use this experience to learn about yourself. meet and talk to new girls and keep your relations with the other girl casual. if having feelings for someone of the same sex is new to you, it would benefit you to explore that and learn about it. i don't think it will do you any good to go through the rest of your life ending decent relationships and friendships because you had never learned how to have a handle on it. the important thing is to be in control. instead of focusing 90% of your attention on this girl, only focus 10% or something.
remember that the person who keeps calm, collected, and cool usually comes out on top.