For the past 3 months my throat has been feeling like it is closing up or there is a lump (like when you swallow a pill and it gets stuck).
The feeling you describe is one of the most common symptoms a type of acid reflux called laryngopharyngeal reflux (LPR) and sometimes "silent reflux" because it isn't accompanied by typical heartburn symptoms.
The lump is usually caused by an area in your esophagus that has been irritated by the acid from your digestive system. The medication your doctor prescribed should help the irritated area heal but it generally takes longer than a week (4-12 weeks is common).
You may also want to try modifying your diet by minimizing caffeinated drinks and alcohol, avoiding tomato-based sauces and foods containing peppermint, eating smaller meals and not eating for 2-3 hours before bed. Given time, and medication, the esophagus will heal but you may need to monitor your diet to keep it from recurring.