Is it possible that she is getting fed up of me as I am shy?

I am a 22 year old guy and have been going for some classes for preparation of exams to get into an MBA B School as I am pretty much done with college. There i also got crush on this girl who is also 22 or maybe 23 now. We had a handshake on our first day of class which was on 13th July 2023 and it was the first time i did handshake with a girl. She also was initiating convo with me asking me whether I had lunch or not and some more and I answer her too but I am shy to initiate further convo with her. Today it looked like she is probably fed up of me as I am shy and she is the one who tries to talk to me. We didnt talk today. What hurts is she is hanging around with her friends and 2 of them are male friends too. I am feeling like crying today for being so shy and I fear that I may lose her as well because some guy might become her boyfriend or its even possible that she is probably dating a guy who isn't in our classes. I did improve compared to my school days because in school days I couldn't even keep an eye contact with a girl and not even utter a word with girls as I was super shy but now at 22, I at least can keep an eye contact with a girl and answer them but its still not enough. I don’t even know what to do. I wanna message her on Whatsapp by finding her number from our class Whatsapp group but I am scared about how she would react if I messaged her.