My DD had silent reflux and it was caused by cows milk protein intolerance so was (and still is) on soy formula.
She was about 5 months before we found that out and had her on meds. She was on 10mg of nexium.
The suspension isn't effective and damn expensive. I used to get my half Nexium tablet put it in a tablespoon, pour over cooled boiled water and used her plastic feeding spoon to dissolve it. I then tipped out the excess water and split the remaining tablet with some liquid still in it onto two of her spoons.
I'd also fill a 5 ml syringe with apple juice.
So I'd tip the medicine in her mouth then follow it with some juice and repeat til it was all gone. The stuff tastes awful so the juice was the only way she would take it.
Also try a regular soy formula, we have katicare. If you find that's not thick enough for him (it should be though as it's thicker than milk based formula) you can add a feed thickener.
Or try a lactose free one first to see if it's a lactose intolerance. If not it could be the cows milk protein, in which case soy should do the trick.
I'd definitely suggest also upping the meds too through your doctor, they grow so quick you're likely going to have to up the meds constantly.
Good luck Hun silent reflux is truly awful, but at least you have doctors taking you seriously and helping you out while he's so young, everyone told me it was normal baby behaviour and fobbed me off as an idiot and first time mum who didn't know any better for 5 months!
PM me if you need.