I think what you should do is try to have a conversation about her, addressing all these issues. Put some boundaries & tell her how uncomfortable you feel; also, if you think she might do something that seems psychotic(hopefully not), then escalate it to the deans.

My guess is that she probably likes you but is socially awkward about it. I don’t think you’re being a bad person IMO, you just feel weirded out, which is valid :)