A globus or throat-lump feeling together with gastritis-type symptoms after starting iron tablets often comes from reflux, since oral iron is well known to irritate the stomach and food pipe, especially on an empty stomach. Three months without improvement despite gastric treatment does need a proper look, since globus can persist from other causes too if reflux alone isn't the full explanation.
Next Steps
Switching to an IV iron infusion, as your doctor already suggested, bypasses the gut entirely and should ease the gastritis-like symptoms tied to oral iron tablets. Taking iron with food in the meantime, and asking your doctor about an acid-reducing medicine if reflux is confirmed, may help too.
Health Tips
If the throat lump comes with difficulty swallowing, weight loss or voice change, please see an ENT or physician to rule out other causes.