I am a 23 year old guy who never had a girlfriend before and only been on 1 date so far which didn't work out. I just graduated college 7-8 months ago and planning to go for MBA degree next and going for several classes for now. In the classes for the past 1 month, I got crush on this girl who is also within 21-23 age range. I had been shy near girls in person throughout my middle school, high school and most of college days too except my last year of college. I was too shy to even keep eye contact with girls in my high school days and pretty much never interacted with them so I had very limited experience with the opposite gender until the age of 20 or 21. Now at 23, I am much better but still kinda shy near girls at times. So coming to my crush now, I was shy to talk to her too but with the help of my friends and one of her classmate I could finally talk with her and after that I have been able to talk to her and we have been talking briefly several times. We don't get to meet daily as she is in a different classroom. The last time we talked was yesterday and she always smiles when talking with me and we did handshake too and I am getting to know more about her.
I honestly feel butterflies while talking with her because she is so pretty and its one of my super rare times talking so freely with a girl in general. Even saying her a simple Hi feels like a huge achievement and I feel so happy and later brag to my friends that I said Hi to my crush, I talked this and that with her etc and my friends too tease me for fun. But in reality, she is a very pretty girl almost model like whereas I look really nerdy in my glasses. I do make good back-brushed hairstyle but I am slightly chubby so idk whether I look good enough. I am like 5'9 or maybe 5'9.5(about 174-176 cm range) and she is about 5'6(167-168 cm) and my height is above average where I live so I don't think my height is a big problem as I am taller than most of her male classmates and some of them are even shorter than her. But the main thing is the looks. I look slightly better without my glasses but need to wear them as I have pretty high power. Plus I am still not fully sure whether she is even single or not. Even though many people who knows her does say she is single, one of her classmate several weeks ago said she probably has a boyfriend. I didn't ask her that as we still don't know each other fully. I really wanna ask her for hug or maybe ask her out for a lunch but I am scared of rejection obviously. Got rejected by some girls recently too. What should I do? Should I keep any hope? Honestly even if I have a bad day, talking with her makes my mood much better.