If I show this to a psychologist, what would they probably tell me?

Your problem may just be low self esteem. He/she a psychologist or a therapist can help you build your self esteem. You really should send the email it is excellent and she deserves it. After you have sent it and she reads it she will probably thank you for the email. That should open up communication with her or even make you feel good enough to say hi to her whenever you see her.