It is said that hamsters that haven't been handled much aren't normally*tamed, and they frequently bite if you try to pick them up. Also, it may be a crazy idea, but I've heard some hamsters could have fleas if you'd allow them to go out. This is what I usually have for my cat
10 Best Flea Traps Reviewed in Detail (Jan. 2022) But, as Lilafernim said he may not be sick and it could be just a mood.