MFA programs and erotica

Hi! I'm a recent college graduate (I have a BA in art history). I've been writing for almost ten years. I have published three short stories in small literary magazines in the past year, one of them paid. Everyone in my life enthusiastically tells me I'm good at writing, but more importantly I really enjoy it.

With all this in mind, I'm considering applying for MFAs for fiction next cycle. The main reason I want to is that I think it would be really good for my writing to spend 2-3 years with it as my sole focus. I would not be going into an MFA expecting to get an academic job. I would only go to a program that is fully or almost fully funded.

Here's the "problem:" while I do not exclusively write erotica, I gravitate towards and write a lot of it. It's not the kind of thing you find self-published on Amazon, though I'm not aiming to bash those books and authors. I would say that what I write is more similar to something you might find in any literary magazine, it just also involves people having explicitly described sex.

Would I be able to pursue erotica in an MFA program, or would I need to do that on my own time and explore other things in school? Would it even be considered appropriate to share that work with my classmates and professors? I want to stress that I am not exclusively interested in erotica, but I want to know what my options are going into an MFA program. Are there any programs out there that might be a particularly good fit?

I think erotica can be and deserves to be taken seriously. Sex is a deeply important part of life, and thoughtful writing about it is worthwhile. That's why I write it. I'm not interested in making a ton of money. Would an MFA program help me write better erotica?

Thanks in advance for any advice and opinions.

EDIT: Hey y'all! I got such good and helpful comments on this post, thank you! It's looking like an MFA probably won't be the right fit for me the more I think about it. While what I write definitely has a place in those programs, when I think about the writers who I admire, who I want to write like, hardly any of them have MFAs. I think what I'm most interested in is taking genre fiction seriously. My dream novel project doesn't fit well into what MFAs seem to encourage. I don't know how to articulate exactly what I mean without showing you all my work, so you'll just have to believe me. I'm going to keep thinking about it, and I have almost a year to do that, but in the meantime I'm going to work on my lesbian detective novel and not worry so much about the degree. Thank you all again!