WELCOME to YT! She is just adorable
. If you truly think she may have hearing issues, I'd definitely have the vet check this next time you go in for shots. Otherwise, this might just be normal puppy behavior.
Her eyes may be teary bc she is teething...the teary eyes may come and go throughout puppyhood as she intermittently goes thru teething.
As for the puppy class idea - GREAT idea, it'd be really good for you both. Just make sure you don't enroll her until she has completed her puppy shots.