Baby might be allergic to formula ?

My Lo is a month today, when he was born the hospital provided similac advance for him and he couldn’t keep it down, he would throw it up so the pediatrician at the hospital decided to put him on similac sensitive (orange can) . He was drinking that one for about 2 weeks until wic told me to try again the similac advance ,which sounded totally stupid to me after a DOCTOR switched it. But I decided to try it again and as soon as he started drinking the bottle he threw up. Ever since that we stuck with similac sensitive & ive kept a close look to his symptoms since i knew something might be wrong if he cant keep down certain formulas. Well his symptoms have now been that he wont burp, i try different positions and nothing makes him burp and well all the gas stays in his tummy and he looks bloated. He gets fussy and try’s to push like if he’s going to poop but doesn’t, and when he does poop he poops once every other day which is like diarrhea. He still throws up but not as often and I thought it would go away but hasnt and thats why im worried . I did some research and i found those may be symptoms to an allergy including dry skin but I thought it was normal newborn skin.

I dont know what to do to help him but I already made an appointment with pediatrician, has anyone ever been through this ? 😞 im a FTM and i feel like im failing at this new motherhood thing 😢