Some bacteria are immune to some of the most commonly used antibiotics. Unfortunately, you don't find out whether the bacteria causing your sore throat is immune until after the antibiotic has failed.
An allergy test sounds like a good idea. If you do have an allergy, your immune system has to work harder and if the allergy hangs around a long time, this means that your immune system can overwork and get stressed out.
Another thing that happens with allergies is increased mucous production which normally helps the body rid itself of foreign bodies [allergens]. Unfortunately if there's too mucous being produced, or if it can't drain away completely, this creates a perfect breeding ground for 'opportunistic infections'. This just means that bugs which normally wouldn't trouble you now have a perfect home to hang around and breed.
I've had seasonal plus year-round allergies for many years. Whenever my allergies acted up, I'd often get opportunistic infections. Since my allergies have been under control [thanks to allergy shots], I rarely get throat infections.
Before a cancer diagnosis is made doctors usually want to make sure that they've eliminated other possible causes. This is mostly because cancer therapy is in itself quite dangerous.
Ask your doctor whether you might have chronic sinusitis, because that usually takes a much longer course of antibiotics than a regular throat infection and sometimes the only symptom is a sore throat that keeps coming back.