I agree with red panda. Don't get caught up in labels. Bipolar looks different for different people, and so do all the rest of the disorders. You need to find a way to live happily regardless of whatever disorder you might present. I was told by a therapist once that she doesn't treat disorders, she treats symptoms. That's what you need to focus on.
As for all the fights with your girlfriend, when me and my husband first moved in together we fought ALL THE TIME. This was before mine and his collective dx's. maybe you could try couples counseling as well as getting your own therapy.
I do understand your pain and I truly hope it gets better for you