Detergent For Chin Fleece

I have a bit of a problem right now. My chin has a weepy eye and gets drops as needed (he was at the vet last week and his mouth is fine). He obviously hates the drops, so after he gets them, he will rub his face on the fleece I have for him.

I can't help but wonder if the detergent I'm using to clean the fleece is aggravateing his allergies. Which detergents do you guys think is safest for chinnies?