Hi K.!
AH the teething stage!
I can't recall my son drooling as much as your baby seems to be, so I can't remember if he was quite as chapped...BUT I would like to offer some products that I remember using, (still do) on his chapped cheeks and skin...you may have tried them already, and I would definitely ask your doctor, in case it is ezcema, but there is Baby Magic, by Playtex, a daily protection lotion for faces, says it helps, "protect against sun, wind and DROOL". It's PABA and fragrance-free. SPF 20 so good if you take your baby outdoors. All it says is to ask a doctor before use on children under age of 6 months. So that's your call. I even use it on my face when we're out in the sun. AND to this day my lil man has the driest skin, well dry face mostly, and after his bath, I use Johnson's Baby oil, BUT I use the one that's in a spray pump, so I spray a little on my hand and soak it into his cheek's. I've been using that for a couple of years on his face now, and he's never broken out or anything, and it only takes a tiny bit. I don't like him sticky! And the only other thing I can think of is good ol' Vaseline Petroleum Jelly, (even great on sore lil cheekie-butts, if you don't have diaper rash cream on hand). But maybe just use it during the night, or else everything will stick to the areas you applied it to! But it works so well overnight on sore noses, or dry dry skin! And it's very safe and repels moisture and is fragrance free. I don't know. But these are just suggestions. Since your baby boy is still young, it's always best to at least call the doctor and see if they have any advice over the phone, they may want to see him, and then they can go from there! Hope it all works out for you. We don't like when our children are uncomfortable!!! Good luck!