You'd probably have seen symptoms way sooner for CMPA. You could try stopping milk until all symptoms clear up, and then reintroduce it. If symptoms come back, there may be some intolerance
If they've been fine on formula it's very unlikely to be CMPA as they would have had a reaction to this as it's derived from cows milk unless you get the specific goats milk one. If theyre unwell it's probably from that.
I’d say you definitely need to reevaluate after his illness has gone
My son is highly allergic, symptoms even while breastfeeding as early as 3 months old, had to have me stop eating/drinking milk, and he couldn’t have hydrolyzed formula, only amino acid. I agree there should have been earlier symptom, rash, diarrhea, hives, etc. Since he’s had milk in food already and more than once. Or it could be a smaller allergy, even adults can get allergic to something all of a sudden.
Could be coincidence, could be the protein. Not likely to be lactose sensitivity since it's never been an issue before. Cows produce one of two types of protein. A1 or A2. A1 is most common but slightly harder to digest, A2 is easier to digest but less cows make it. A few things to think about, you can look for A2 or A2A2 milk and try or wait until after his viral infection is over and try regular milk again. If it is the protein sensitivity, likely the formula and cooked foods denatured the protein enough that it was never a problem before