What mistakes did I make and how could I correct them next time?

I was in the library studying and I saw this cute girl pass by and she said hi to me. I was a bit confused since I didn't think I knew her. A bit later I approached her said hi back, asked what she was doing she told me what she was studying and then I asked her if I knew her from somewhere.

It turned out that she was sitting right next to me in the library on Wednesday when I was studying for a test. She remembered my name and my major (I'm in university) but I didn't remember her, it felt kinda weird asking her who she was.

I asked if she was interested in getting coffee sometime and that I thought she was cute, I asked for her number but she insisted on getting mine instead.

I realize that she is never going to text me, but I would like to know what I did wrong.

Was I being too forward by telling her that she is cute and asking her out for coffee?

Strangely enough I don't feel so upset, on the contrary I am happy since this is the first time I had the courage to go up to a girl and tell her I find her attractive and ask her out.
+1 y
By correct my mistakes next time, I mean with the next girl I approach.
Also if I see this girl again should I talk to her or not?
What mistakes did I make and how could I correct them next time?
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