Milk allergy

What were the signs your little one had a milk allergy? Our little one is 14months. Hes been absolutely fine on formula. When he turned 12 months we started to introduce cows milk for his bedtime bottle (hes been having milk in cooking ie mash potatoes, scrambled egg since around 8/9m and has been fine - his HV approved this). To be honest I think I went too much too soon and his stools became loose, not mucousy, just looser. We then decided to slowly transition his bedtime bottle by mixing formula and cows milk. Everything improved. Recently he has been having more dairy and his stools are loose again. We arent sure if this is because of the dairy or just because hes been so full of a cold with lots of phelm (my parents said they get an upset stomach when phelmy). We've cut back on dairy to see if it helps. Just wondering what everyone else has experienced. Please be courteous, Im a FTM and still learning.