Vomiting after cows milk

My 13 month old has been EBF. He only enjoys water out of a sippy cup. Everything else causes him to gag and then instantly projectile vomit. I have avoided giving him anything but water in his sippy cup.

I have tried pumped breast milk, almond milk, pea protein milk, pedialite and cows milk off and on over the past few months.

Today I tried cows milk again. He didn’t look like he hated it but then instantly vomited on the carpet and then picked up his cup to drink more (which I didn’t let happen).

Anyone else experience this?