I have a sore throat that feels like a tickle. I keep coughing but can't clear it. Gargling hurts!?

? allergies. Your symptoms suggest allergies or an irritant of some kind. Tou might try an antihistamine.
Possibilities... A good possibility is that your cough is due to post-nasal drip which could certainly give you a "tickle" in your throat resulting in chronic cough. The best treatment is likely to be a nasal spray that your doctor could prescribe. So, see your doctor for evaluation so this treatment can be initiated. Other possibilities include gerd and bronchospasm which have different treatments.