Does my hamster have mites?

It definitely sounds like mites. He could have gotten them from his bedding. Don't worry, mites are not immediately life threatening but if left untreated can get pretty bad. There are a few ways to treat it. There are all sorts of flea medicines for dogs, cats and small animals that you can find at your local pet store. Try to get one that is drops that you apply to the back of their neck. Powders can also work but the drops are the best. Some sprays are good, but as you said it is hard to get the animal to hold still and hard not to get it in their eyes. For the drops, powder, or spray, I recommend putting your hamster in a small box or tub and trying to apply it that way. It may be hard, but remember, your helping your hamster.