Food Allergies Treatment

Hi,
My son is just over 4 weeks old and cries all day when awake; its very rare that he has anytime awake when he isn’t crying and seeming in pain. Our GP thinks he may be colicky so suggested we try infacol which didn’t seem to make much difference (we’ve also tried all the anti-colick bottles going!). We changed his formula from cow and gate comfort to aptimal at the beginning of last week which seemed to calm his belly a little but didn’t stop the crying! We saw a paeditrician on friday about a seperate matter and he suggested he may have reflux so prescribed infant gaviscon; and guess what? the belly ache has returned with a vengence and hes now constipated too! So we are going to stop using it as its made him worse rather than better.
I was wondering though if anyone knows what symptoms come with a milk allergy? He’s not a very sicky baby (he might throw up a mouthful after a feed but thats it) and he’s putting on weight well so far. However, he does get a lot of diarrhoea, belly ache (like colick, with a red face, pulling legs up, etc) and he also has a rash all over his face, shoulders and chest which the doc says is milk spots but look quite severe to me. As i say, he also cries constantly whenever hes awake. Do you think he might have a milk allergy? What symptoms should I look for?
Thanks for your help!

My baby is coming up on 5 months. My baby is/ has been colicky, spits up frequently, sometimes 2-3 times after every feeding, violent explosive poops, green poop, slimy poop. She used to poop every other day, now she poops 5-6 times a day. I think it is diarrhea. How did you figure out it was a food allergy and what did you do about it?