Fussy baby! Help

FTM here and embarrassed that I don't know but my baby seems to be fussy and unhappy when hes awake. Only happy when eating and sleeping. Sometimes he will lay on play mat for about 10min before needing to be held again. (Not a wet diaper issue or rash issue)  
I have talke to pediatrician and he said to keep breast feeding and supplementing when he is obviously still hungry. 
I'm wondering if he needs a hypoallergenic formula for protein breakdown issues. He is getting better but still seems so unhappy. He doesn't spit up and sometimes has gas.