Toddler licking his hands

My 2.5 often licks his hands. He repetitively licks his fingers and puts his hands in his mouth wiping them down his chin so the skin on his chin gets red and irritated.

Has anyone else dealt with this? He is not teething. How did you address it?

I’ve already explained that it is hurting the skin on his chin and can make him sick spreading germs. If you tell him to stop he seems to do it more! We’ve already had multiple illnesses since he started a few months ago (colds, gastro, etc).

Thanks!