I’ve been talking to this girl for 4 days and I’m worried she’s not stable emotionally

We’ve hung out a couple times, nothing has happened yet, she’s extremely into me and keeps calling me cute and handsome and she’s also the most genuinely sweet girl I’ve ever met she’s actually like a very pure good person. I’m afraid she’s in too deep and that we’ve moved very fast. It seems like no matter what I’m doing in my day I’m in consistent contact with her all the time. She’s going into college in a couple days but thankfully it’s a college with no frats or Greek life at all. Idk if I’m able to give her everything she obviously wants from me. She’s already talked abt me taking her to homecoming which is over a month and a half away. She’s amazing I just feel like she’s too into it or too attached already. I’d hate to break her heart but she just doesn’t seem very emotionally stable. It’s gotten to the point where I feel like she’s obsessed with me. She’s also a little clingy even 4 days in. I just don’t really know what I should do.

If anyone has any advice or past experiences I could learn from please lmk in the comments.

Thanks yall