Is it normal to be thinking of someone i don't know?

you almost have the same situation as me.
I have a problem sort of similar to yours where i know this girl, sort of but am a little afraid of what she might say or think if i asked her out.
Of course the rational thing would be to just ask i mean the worst that can happen is she says no.

dont lie just be confident when you talk to her lean slightly back(an i mean barely noticable that u leaned back) it registers as a respectful guy in the minds of women
and dont just ask flirt a tiny bit first(lite flirting not the heavy stuff that gets you slapped) and if she responds well then ask her for her number but say it in a less pathetic way than "can i have your number?"

If you don't mind lying, tell her that she looks familiar andask her where she went to high school, once she says the name, say "me too!" and she'll think she just does'nt remember you. if she has a yearbook, say you weren't there for yearbook pictures. Then come up with conversation and ask her if you two could catch up some time.

Or simply just ask her.