I'm a mess with my feelings and this may be creating me academic problems

Hello, I’m actually not sure in which category should I put my problem…My mind is a real mess at the moment and it comprises several kinds of “problems behind”. I hope I make sense…This is a mixture between silly, but distressing, feelings and academic pursuits. A little bit about me: I’m 22 years old, female college student. I’ve been dealing with the loss of close people from my family and also rejection. I won’t get much into it: It’s just to say that I’m feeling especially fragile at the moment and also very insecure. This is basically my mindset at the moment. One of the things that happen lately – and this is the problem I’m bringing here – was with a professor of mine. Once the classes with her finished I sent her an email asking if she would show me a little about her research; she nicely did and in the end I just asked if I could join her sometime in the field. Despite the promise of sending me an email to let me know, the months passed by and she never said anything. A week ago I sent her an email just to let her know that I’m still interested. She didn’t answer. The most obvious reason is that she completely forgot and/ or that she is way too busy. But this really hurts me… And now that's when I mix this with feelings that I'm not supposed to have.... I feel a slight attraction to her and I don’t know if my shy ways or looking could make her feel uncomfortable. That attraction is just because I’m feeling so lonely and insecure, I’m sure, and I don’t really want to produce a problem; especially when I’m interested in her research. Probably this part is just in my head… There is the rumor that she is a lesbian (this fueled my attraction) but that doesn’t mean nothing. Maybe I did act wrongly in some points because of this ridiculous attraction… E.g.: i) when asking if I could join the field experiments, I told that I would like to go with her (I could go with her team; they weren’t available at the time anyway). But perhaps any shy person would prefer to go with someone they already know, instead of others. ii) I looked at her more than I should at some public event (I guess that she noticed in part…); she also looked but when I met her gaze she, very fast, looked in other direction. Cleary uncomfortable… Should I try to speak with her in person about going with her or simply let it go? I really don’t want to impose myself but being ignored and not being able to know more about this subject makes me very unhappy. I also should avoid what I feel – I guess that this prevents me from thinking clearly – but I can’t help myself at the moment. Thank you for reading this and for any help you may provide!