Is there a medication I can take to stop having to clear my throat?

Maybe. You may have acid reflux which is treated with medications. This may help your symptom. Go see an ent.
Acid reflux/Nasal. I see many patients with chronic and persistent throat clearing. It is generally acid reflux or post-nasal drainage. You can try some simple over the counter meds for acid (zantac, prilosec) for 1-2 weeks... If it improves... Likely gerd.. If it persists see your local ent.