You can try alobaby milky lotion, it works for my girl from birth till now 4mths cos her skin is very sensitive. Always got small red patch around her mouth especially now drooling. I will reapply little amount for her when able. Even heat rash at neck also works well.
It’s common to get milk/heat rash at that age. Just clean gently with a damp cloth, and it usually goes away in 1-2 days
Lennie Pedrozo