how to request?

I want to ask my professor to write a recommendation letter for me. Is it a polite request?

Dear Dr. X

Thank you in advance for sparing time to read my email.
I hope you remember me, the student who drew those teddy bears! ( I drew something for her which she liked and always remember me by those drawings. so I prefer to mention drawings to help her remember me :) is it ok? - Yes)
I passed X and Y courses with you and got A in X and A in Y.
I would appreciate if you would do me a favor and give me a recommendation letter to apply for Z university.
I think the recommendation forms are online. Be certain they are online. Better yet, include a link.
Let me know if you have enough time to fill out the form for me. Having time to fill out a form may not be their only objection. It would be better to ask "Please let me know whether you are willing to recommend me to the university."

I'm looking forward to hearing from you.

Yes, I think this would be a polite request.