I'm thinking about putting my hamster to sleep?:(?

Well,first off,he started off to be a really happy hamster.Now,it has been a year,and he somehow got mites on his ears and maybe body.His ears are getting crusty and his bottom is losing fur.This might not be a good enough reason to put him down,and i know that it would be unfair,but,i'm just a horrible pet owner...My parents will not help me.I told my dad i would pay for the veterinarian but his excuse was "I don't have time." My mom just doesn't care.I just want to put down my hamster because,he might feel so uncomfortable right now and i don't want him to suffer anything that will happen in the future.Should i put down my hamster?:(