I have sore throats frequently and nearly always they are caused by a post nasal drip which is caused by allergies. It is prime allergy season right now. I use a cortisone nasal spray to help with the allergies. I've also take OTC decongestant/antihistamine combinations that helped. My go to product is Sudafed, the original one that you have to get from behind the counter.
If you still have a cold or a sinus infection you will also have a post nasal drip. That will cause a sore throat. A decongestant will help with that. Sudafed, the original, always clears mine up in a few days.
I can feel the post nasal drip. It's a sort of squishy feeling behind my epiglotis, the piece that hangs down at the back of the mouth in front of the throat. And I often have no other symptoms. What symptoms you have depends on your particular body's response to the allergens.
I would not continue to take antibiotics. If your sore throat is caused by an infection it's nearly 99% certain to be caused by a virus. I'm surprised that they gave you antibiotics. The doctors at my clinic and my daughter's clinic do not give them for a sore throat unless we've tested positive for strep. There is a quick test that can be done while you wait.
And I frequently wake up with a sore throat because I'm a mouth breather when asleep. Most days the soreness goes away after I eat or drink something but not always.
Know that if your throat is irritated because of the cold, it will be more sensitive to other conditions.
I urge you to stop considering that it's cancer. What are your environmental risks? Unless you've been a heavy smoker for several years it's highly unlikely for you to have throat cancer.