Son has thrush. What to do about his hands?

He constantly has his hands in his mouth! He HATES pacifiers and won't take them. Also he's teething and he has excess amounts of drool. But what should I do about his hands as I'm afraid we won't get this cleared up because of the possibility of it being on his hands all the time. New mom so I'm lost. We're boiling and everything like that and washing our hands or using hand sanitizer constantly because he chews on our fingers and hands. Thanks.