Looking for advice or insight

Hey, so I just found this community and felt like I had to get this off my chest. Personally, I'm not sure whether I fall under the HLM category, nor that my girlfriend falls under the LLF one but here's the deal. But we seem to have a similar dynamic.

We met each other a year ago for a single date after which she turned down a second one. A couple of months late, however, she reached out to me again and we started texting, went on a few dates and things happened. We've been in a relationship for 10 months now and it's been a rough one, especially in the beginning. At this point, I must say that she's had a couple of pretty dysfunctional and rather toxic relationships, and while she never went into details, that's the general impression I'm left with. Aside from that, she also has a very unhealthy relationship with work — long hours, constant stress, and lack of enjoyment from what she does. Mind you, she's in the creative business, and I know firsthand how important the latter is for one to feel capable and productive.

Anyhow, I don't know if this background information is of any importance at all but at the beginning of our relationship, she obviously had trust issues. She wouldn't share any of her feelings, wouldn't initiate dates, and sex was also absent. We wouldn't have sex for days and even weeks. She would sometimes accuse me that it's my fault that can't get her in the right mood, which was very tough. I generally felt unwanted and unappreciated. However, things slowly changed, and although she's still not that initiative in any of those things, I can feel that she actually loves me — we've been spending pretty much every single day together and long for each other when we're not around each other. But sex is still a huge issue for us. Partially, I blame myself for it and I'm angry at her for not communicating honestly and openly with me. To illustrate, I recently found out she has HPV 16 through a gel hidden in the bathroom, even though I was told that her checkup went fine and there's nothing to worry about.

Aside from a couple of two to three-week-long periods, where our sex has been frequent and amazing, we haven't had that much sex. There were times where I initiated it and she doesn't seem into it and other times where she initiates it but at the same time, it's obvious that she's not in the right mood. I can tell because I know how she is when sex is really desired on her end. At some point, I also recognized that sometimes during sex she seems to be in pain, though she was very good at hiding it. It took me some time to figure all of this out. But on my own, mind you — she never talked about it. After every failed attempt or bad sex, I would try to talk to her, but she just stayed there silent or confused about what to say.

A couple of months ago I had a conversation with her about it and told her that we don't have to have or try to have sex if she's not into it. This seems to have lifted some of the stress around this but hasn't at all resolved the issue. I've read a lot about what may be causing it — low libido, some form of dyspareunia (because of the pain), emotional trauma, asexuality, you name it. But I don't know what it is and she doesn't seem interested in finding the reason. I don't know if this even is something I should expect from her? I don't even feel comfortable with trying to talk about it because I'm the annoying one that always brings up the issues in our relationship and does his best to resolve them. I've tried to suggest therapy, both mutual and solo — didn't result in taking an action.

Anyway, I'm at a point where I don't know whether I should stay in this relationship, although I love her so much. But the lack of initiative towards a healthier form of communication and problem-solving is killing me. Have any of you had a similar experience? What are our options? To me, it seems more complicated than LL but I might be wrong.