Hi there and welcome to BW!
Lucky you to have such a wee baby STTN! It's pretty normal to still have to feed 3-4 month olds during the night. Given his background, it could be a number of things. I was wondering if you could post his routine in this format.
Wake up
E 7:00
A
S 8:30 to 10:00
E 10:05
A
S 11:30 to 1:00
Etc.
My first thought is hunger and its what I would address first in such a young baby. Young babies have so many gs that this is usually the culprit. Given that he has reflux, has his meds been adjusted? As he grows, he will need some adjustments so if he's getting more spitty or is arching,etc during or after feeds, then I'd go back to the dr. Seeing his routine will give us some clues as to why he might be waking during the night.