Do not let the DRs tell you they are out of ideas. Please discuss using other PPIs.
I will tell you that it took a considerable push for me to finally get a GI to treat my daughter. At the lowest point she'd stopped eating completely (she was almost 11 then and had lost about
10 lb). I took her to the children's hospital ER on the morning of her 2nd day of refusing to eat. Even though our regular ped had referred her to their GI clinic, they hadn't returned any of my calls. At the ER, the triage nurse figured we were there for a GI consult and said she couldn't get them in for that, considering my daughter wasn't, you know, vomiting blood. But miraculously a week later the GI clinic called to set up an appointment.
From there we went through prilosec, prevacid and finally dexilant, after an upper endoscopy with results similar to your son's. Everyone reacts to ppis differently and that's why there are so many different ppis on the market, both over-the-counter and prescription. If one doesn't work, try another! You might also experiment with quick-relief antacids. My daughter gets no relief from Tums but does find Ma'alox works well for her.