Hi Amyboo
My DS was born at 31 weeks and spent 6 weeks in neonatal. Came home with undiagnosed silent reflux and it sounds very similar to your experience, thought we didn't have the vomitting, just the discomfort, very difficult to feed and wanted to be held all the time. Basically, most of the issues are due to immature digestion, it is very common in prems. I would go back to the paed and try to get some better medication, infant gaviscon does very little imo. I used omeprazole, which blocks stomach acid, so helps with the cramps and discomfort that they often feel. There are other meds that can help with the vommiting but I have no experience of those. We also used a prescription formula (Aptamil Pepti) which is for Cow's Milk Protein Intolerence, you can achieve the same results but cutting out dairy if you are breatfeeding.
When you make any changes, try meds etc give it a few days to see if it's working before you change or stop.
If you try omeprazole don't get the liquid, it's rubbish. The tablets are much better, though they are a faff to give. The trick is to dissolve them in a tiny bit of sterile water and then use a syringe to suck up the liquid and dissolved tablet and give it to your LO. Don't dissolve in milk as that doesn't work. There are a few support threads for reflux on MN that should help you.
I bought a sling and used that a lot to get stuff done, get out and about as DS was a velcro baby. I think they just need the comfort so much when they are struggling with feeding.
I weaned at 6 months, four corrected. It was a very slow process so food only really properly replaced milk at about a year.
It does get easier, they do grow out of it and you get your life back!