Been dating a girl for three months, she says she likes me but doesn't show it

I've been going out with a girl since January, we first started talking two years ago but finally met up at the beginning of the year when we started going out. She's told me that she likes me but she keeps saying "we're only close friends". I have very strong feelings for her and I've tried to show her how much I care about her but it's like she denies it all. She keeps mentioning her exes and dumps a lot of her mental health problems on me (including her suicidal thoughts), and it really stresses me out and makes my own mental stability worse, and I can't be the only person to help her out.

She's basically said she'll be locking herself away and feel under control if I were to become her boyfriend, even though I've tried to tell her I won't be anything like her exes, and showed her this too. We've done basically everything in just three months that couples would do - including have sex - but I don't see her as a friend or a FWB, I want to be with her and I'm tired of feeling like she doesn't love me. I can't do this anymore, do I try to rectify this situation or move on?