Definitely see a paediatrician if you think there is a milk protein allergy. My son has one. Soy formula is recommended for use with babies over 6 months old. I'm not sure why. Even then up to 50% of babies with cows milk protein allergy have an allergy to soy, so soy isn't always the answer for babies with cows milk issues. There are goats milk formulas (not sure on the age recommended) but babies who react to cows milk protein react to the similar protein in goats milk as well. The alternative for allergy babies is a prescription formula which eliminates the cows milk. A paediatrician would be able to help you work through if there is an allergy and which formula suits.

Good luck on getting it sorted. I know feeding issues can be really stressful so be patient and kind to yourself