DD2 is MSPI and has terrible "silent reflux." She used to cough/gag whenever she was on her back. She never had trouble gaining weight, and she rarely spit up - well, it rarely came all the way out. Silent reflux is where they spit up, but swallow it back down. It's actually worse than classic reflux because it burns their throat going up and coming back down. While newborns nurse frequently, in general, reflux babies often nurse even more because it soothes their throat. But then they reflux and it hurts, so they nurse more, etc, etc. It creates a vicious cycle.
I would give the reflux meds some time to work. DD2 started on Zantac, then we switched to Prilosec, then to Prevacid. Prevacid finally worked.
You can try cutting major dairy, as dairy can aggravate reflux. But I wouldn't go completely dairy/soy free at this point. I'd see if the meds start working after a week or two. Also, try to give the meds 20-30 min before feeding LO. Burp her well, and keep her upright as much as possible.