I would make sure that you describe exactly what his episodes look like. Also, it really helped us to videotape an episode so they could see that we weren’t exaggerating (we got a lot of pats on the back and “oh you’re just worried first time parents” until the ped actually saw one of Kaelyn’s episodes).
What type of formula is he on? Kaelyn had similar episodes early on. She would spit up and choke on it, turning blue until it cleared itself. It turned out that part of her problem was the alimentum. Apparently, it is slightly thicker than nutramigen and it was sticking in her throat.
Good luck with the specialist!