Research the PetArnor topical flea and tick treatment and see if there are any other reports of skin problems attached to it.
I'm afraid I don't know, as I am in the UK, and don't know that product. But I do know that some products are worse than others for various reasons.
If I were you I would definitely let her vet take a look at that.
It couldn't be ringworm could it? (which is a fungal infection, not an actual worm.) Ringworm can leave circular lesions, hence its name.
If it is, there will be a medication to treat it. Speak to the vet.