The last few times I've gotten pied with shave foam, my cheekbones and nose get quite red for about a day or so after. Could be a mild allergy or cheap product...

Adding moisturiser after usually results in a mild burning sensation.

Anybody have any go-to's that help with this kind of thing?

Make sure it is just original and not menthol.That tends to burn and leave skin rashes if on for too long since it is designed for cooling.

The shaving cream is drying out your skin, so you'll want to treat it as soon as you can after you clean up. I've started to do that after my shoots, which feature lots of pies, so I'm always dealing with eye and skin irritation. I'll rub a skin cleanser, moisturizer, toner, and facial serum on my face just to restore some of the nutrients it needs to recover and minimize the lingering eye irritation that comes with having foreign items near the eyes. You probably don't need all of those things, but some combination of them does help. The burning sensation with shaving cream is sort of inevitable.