I think the reason why she is "flipping out" or "flipping back and forth" so much is because you guys only started talking last year in October and since that time, you have literally moved across states to be with her. That would make any normal person "flip out" because that relationship went from 0 to 100 real quick.

Take it Slooooower.

You need to take it even MORE slow because she has mental health concerns right now.
You can't jump into a relationship so quickly like that and expect it to be all wonderful. The fact that she said she told you she loved you too fast, isn't her mental illness, it's her being honest with you because you guys did move really fast in the relationship.
She already told you she is 'falling in love with you' which is a good sign.

So stop "stressing her out" every few days, or whatever you said. Give her space and time, sounds like that's what she's trying to tell you. Just be there for her whenever she needs you, but don't smother her. She needs to get her own emotions and her own mental health stable and it's hard to do that while you're in a brand new relationship that is moving at lightening speed.

Good luck with everything.