Why can't I quit clearing my throat and coughing?

Possibility... It is possible that post-nasal drip is the etiology of your symptoms. There are very effective prescription nasal sprays available so see your doctor for evaluation and treatment.
Post-nasal drip. Post-nasal drip is a common reason for feeling like there is something in your throat, leading to repeated clearing of the throat. Cough is the body's effort to keep the drainage out of the lungs. If your symptoms persist for a week or more are associated with a fever or pain, i would suggest seeing your doctor.