If bathing, just hold his head so he can't lick. Not all dishwashing detergent would be perfectly safe. Dawn Original is ok. You would just be killing the ones crawling on him though. It does not kill eggs.
You should not need a vet appointment if you're sure it's fleas. Most will sell it to you without. Frontline is fine to try. Yes, chemicals can be harmful, but personally I'd rather put chemicals on my dog than have her uncomfortable and an infestation in my house.
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