Woman I'm seeing claims to like me, but it feels like our interest levels are mismatc

I have been seeing someone for a few months after meeting at university. At first, I thought we'd only be friends, as it didn't occur to me that she'd be interested in that way, plus she confided that she was struggling being single after a very tumultuous summer during which she had a chaotic fling with an older prof. That set off alarm bells, and I remember secretly hoping she wasn't looking for a rebound, as she obviously needed time to get over him and learn to become comfortable with being single.
Very quickly, however, she began ingratiating herself into my life: inviting me to hang out outside of classes, inviting herself back to my place, initiating kissing and sex (after hanging out 3 or 4 times, which personally feels fast), texting a lot. She eventually asked if I wanted to date, and I agreed, as I managed to convince myself that everything she said and did was indicative of genuine interest in me as a unique individual. She said that she isn't ready for a relationship, since she tends to get heavily invested in the other person. She said she might be in 6 months. I accepted, and we began seeing one another more regularly and intimately.
Mind you, I never stopped noticing her red flags: untreated bipolar resulting in a recent manic episode (and fling with a guy twice her age), her pushiness regarding hanging out even when she knew I was on a tight deadline, her overly familiar relationships with male friends, her tendency to take exaggerated offense to innocent remarks, etc. However, because she would comment about the future she envisioned and what a great father I'd be, etc., stay over all the time, hold hands with me in public, etc. I believed she was seriously becoming interested in something committed and long-term, so I looked past flaws.
A month into dating, the subject of seeing other people came up for a 2nd time - a question we'd both answered in the negative a few weeks prior - and she admitted she'd gone on a date recently. She quickly tried to minimize it: she said they'd met at a party that summer but that she'd forgot he existed; that it all came together last second; that I "was way funnier"; it was only once; "nothing happened"; that she figured I'd be "a lot more nonchalant" about it since we'd never explicitly agreed upon exclusivity (although she'd previously complained about my having close female friends, which I feel is hypocritical.) What really devastated me was that she left my place after spending the night to go get ready for this date, lying about her reason for leaving (just before we were about to have sex, no less.)
I didn't say anything for about a day, but figured it'd be best to stay on good terms since I'll be seeing her for the next several years. After talking it over, she came back to my place, and we had sex, unprotected (dumb on my part, I know), which she emphasized was a big deal for her.
I felt like the casual arrangement - while not ideal - might be manageable, as we seemingly left on a high before I went home for the holidays. We texted and called for the first few days of break, but she suddenly ghosted for almost 3 weeks. She only called again a few days before classes started to see if I was back in town. Wouldn't you want to stay in contact with someone if you "really liked" them?
Anyway, it's been a few weeks, and I've never felt so conflicted about a woman. Sometimes when I tell her I like her, she'll ask "really?" and not say it back. Other times she'll say it unprompted. Sometimes she'll question why I ask her questions about her future (like where she'll move to once the program is over.) Other times she'll ask me to do something with her that's still a year away, or invite herself when I talk about my ideas for future trips abroad. Sometimes she'll ignore me in class and other times come over, saying she was fantasizing all day and wants condomless sex.
I also don't think I can trust her after her belated mention of a date. When I see another guy - whom she's described as "hot" before - walk around with her on campus, approach her after class, or pop up on her phone (I saw his name near the top of her IG inbox), whenever she leaves abruptly and texts someone as she's walking away, etc., I find myself assuming they're dating and having better sex more intimately and regularly than her and I, that she is Infinitely more attracted to him (he's a classic "bad boy" type) and is merely stringing me along for security to fall back on. I know I have low self-esteem, but it's unclear if that means I'm merely being paranoid or that she counts on me being a spineless loser who'll never refuse her no matter how little she gives me and how freely she throws herself at those she truly fancies.
I feel hopelessly in love, but know this can't actually be love, as I find so much of her behavior selfish and repellent, and recognize my own ambivalence. I want her to want me so much that it's an almost all-consuming distraction, but I know that she's never directly said she wants more than what we have, and that a relationship would likely be strained and miserable anyway.
I've tried seeing other people - ever since she confessed to having a date with another - to better fit the "casual" bill and stop placing so much stock in her, but any success in demoting her in my hierarchy of people for whom I care has been temporary and limited at best. After multiple other dates with multiple other people, I'm still hooked on her.
I've just made a mess of my psyche and life, and don't know what I can or should do.