I recently started a proton pump inhibitor for my acid reflux that happens almost after every meal. my doctor is hoping that it will heal the esophagus in 4 weeks to prevent further acid reflux. how likely is the healing going to fix the issue?

PPI does not prevent the reflux, it only reduces the acidity of stomach juice so the refluxed juice does not irritate the esophageal mucosa and it can heal. Most of the time the esophagitis can heal. Besides PPI, you need to practice antireflux measures: eat frequent, small meals, do not lie down within 2 hours of eating and raise the head of your bed about 6-8 inches with 2 blocks of brick.

While esophagitis is likely to improve, without lifestyle changes the tendency for acid reflux is likely to persist and the proton pump inhibitor will be needed indefinitely.