Hello I am Dr RB and I am a small animal veterinarian. Most skin allergic reactions in cats can be divided into three categories-flea allergy, food allergy and environmental allergies.
First flea allergy is very commonly the cause if adult fleas are found in the coat. The allergy comes from the saliva found in the flea therefore, not many fleas have to be present to cause this. One flea bite will do this and create the inflammation under the skin that you are describing as well as secondary bacterial infection from scratching etc.. Therefore, be completely sure that you have eliminated all stages of fleas (adult as well as eggs and larvae) from inside the house, all bedding, and the exterior of the house as well. Mr. Whisker MUST be on a monthly flea preventative that kills all stages of fleas to be considered protected (my favorite are monthly Revolution or an 8 month Seresto collar).
Food allergy is less common in cats than it is in dogs. Once flea allergy has been ruled out by following all the above recommendations, you can try to feed Mr. Whiskers on a prescription hypoallergenic diet for 8 weeks to see if skin inflammation improves.
Environmental allergy can be diagnosed by your veterinarian via a blood test or skin test..
Honestly, your description sounds classic for flea allergy dermatitis.. I would continue the antibiotics for at least 2 weeks but you MUST remove all fleas.. remember that the flea life completes itself so even if you are not seeing adults, eggs are larvae are microscopic and within weeks you have a new adult infestation.
Along with continuing the Amoxicillin, you will need to remove the inflammation from the skin. Most often this is done with an injectable steroid or an oral antihistamine. The steroid will work better but if you are trying to avoid another recheck, you can try over the counter Chlorpheniramine 4 mg once daily for Mr. Whiskers and see if that helps. However, if no improvement occurs, you will need to make a follow up appointment with your regular veterinarian.