Lactose intolerance vs Milk allergy

Allison • Mommy to Jonah 🐳🌈2/8/18 and Ezra 10/29/2020

So My first child is lactose intolerant we discover after his first birthday my newborn of 5 weeks was so sick we tried 5-6 formulas and breastmilk and switched to lactose free and he is doing better but sounds congested and has watery eyes so I worry about milk allergy. Anyone who dealt with either what was your child’s symptoms?