Caught in My Own Web of Desires

So yeah, I've been this college professor for a while now. Mid-40s, divorced six months ago after catching my husband with someone else who was younger than me. The whole thing left me feeling... not great about myself. Like, I knew we had some issues and he'd cheated before too, but that last time really broke something inside. Anyway, long story short, since then I've been throwing myself into work and trying to keep busy with anything to take my mind off things. But one day this student, let's call her Amy, starts showing up a lot in class, asking questions about stuff we didn't even cover yet because she wanted more depth on topics that interested her personally. She'd always seemed quiet before but now here she was practically glowing. I found myself thinking about her more than I should have. Like when she smiled at me with these big green eyes and I suddenly felt this warmth in my chest, nothing romantic, just something like seeing a spark of intelligence that reminded me why I loved teaching in the first place. It's probably fine, right? Just being a mentor to someone who's passionate? But then one day after class she came up and said she wanted to talk about her thesis ideas outside office hours. Nothing sexual or anything, just talking shop and getting advice on research methods. And there I was, feeling all kinds of weird as we sat together in my office while the sun set through the window behind us. Then I went too far, I mentioned something personal about my divorce to try and connect with her, like maybe she could relate or that would make it okay to feel closer to someone. She just nodded quietly and said nothing back though, which only made me more uncomfortable. Maybe she saw right through my little attempt at sympathy. The rest of the day I couldn't shake feeling off. That this whole thing with Amy was crossing some line I shouldn't cross, but also that it could be exactly what I needed, to connect with someone younger and more vibrant who reminded me why life is worth living after a breakup. But it's not her place to fix me or anything like that. So yeah, the next day when we met again for our appointment, I felt this tug between wanting to just get out of there so I didn't say something wrong and also wondering if I should take things further with her. She seemed kind and professional still but I could tell there was something else under the surface too, maybe even a little curiosity about me? It's hard when your mind starts wandering that way, especially after being hurt so recently. I just hope she doesn't read into it wrong or think this is okay, because it isn't. Or at least not in the ways I'm thinking it might be. Just another mess from my end after a messy divorce.