Is it normal that i get easily upset?

I was hanging out with someone that I think I kinda like, and was helping her out with some homework. She got frustrated at me about something while I was helping her, which quickly upsetted me. When this happens, I tend to get sad and quickly withdraw. Well, she eventually asked if I was OK and I said I was slightly sad by what happened, and she said "oh don't let it bother you, I do this to everyone, just forget it happened."

Well, it didn't help how I felt, but I didn't mention it any further; what does help (but I rarely tell anyone this, and I didn't tell her this) is something like a hug or being held. We had (before I replied that I was upset) planned on hanging out again tomorrow, but when she left to go home, I asked if we were still hanging out tomorrow and she said no.

So, I feel like I made her uncomfortable, but I really wasn't sure how else to act; I wanted to be honest about how I felt, without making a big deal out of it. Reminds me that I easily get upset, and why I tend to avoid relationships and people...

Is it normal to get easily upset, or be upset by something like this?