Can a Cat Be Allergic to a Flea Collar?

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I have two beautiful calico cats, one short hair and one long hair. The long haired cat is an outdoor cat but the other has never been outside. I was afraid the outdoor cat might bring home a few cooties to share so I bought flea collars for both of them. This was about three weeks ago. A couple of days ago I notice the indoor cat has a patch the size of a silver dollar under her chin, where she has scratched the fur right off. I cut the flea collar off immediately. It looks so sore and irritated. She keeps scratching at it and licking it. I've been washing it a couple of times a day with warm water but it doesn't seem to be doing any good. I just don't have the funds right now to take her to a vet. Does anyone have any suggestions or home remedies that I can use? I'm at my wits end. Will she clean it herself?