I suffer from crippling shyness

I am a 22-year-old woman and am very much in love with someone who is in class with me. We know each other casually but have never had a conversation. I have caught him looking at me a few times and have felt like going up and introducing myself, but I suffer from crippling shyness. I am convinced he is as shy as me, which makes it impossible for either of us to talk. I can’t ask my friends to introduce us because I can’t even bring up the topic with them. The term ends soon, and I feel as if I will lose my opportunity to tell him how I feel, which makes me sad. Should I assume nothing will happen if he never comes up and says hello?
You have the option of addressing your shyness or accepting that this is out of your control. You don’t know how this person feels and have no means of finding that out until you acknowledge that your actions are driven by your need to accomplish something. You can try setting yourself small goals, instead of looking at the big picture of what this person means to you and whether or not he reciprocates your feelings. Think of him as a classmate first and ask yourself what you would like a classmate to ask you. This can be a conversation about the subjects you study, and all you have to do is introduce yourself. Yes, it can be difficult for someone who is shy, but if he isn’t making an effort, there will be no progress on either front. If he isn’t friendly, at least you will know whether your feelings for this person are misplaced. You owe yourself that much.

I’m afraid of someone who is better-looking than me and don’t know how to be nice around her. What should I do?
Accept that this feeling is normal and try separating her looks from the person she is. Also try and recognise that insecurity comes from within.