IF the lactic acid in fact does something for you, then the doc goofed again, as there’s very little lactic acid in milk – unless you use sour milk! Milk contains lactose (a sugar) and casein (a protein) and fat, but that’s about it. Bacteria that can metabolize lactose by fermentation produce lactic acid – this is why yogurt, keifer or just plain soured milk tastes sour.
BUT, I doubt very much that lactic acid does anything to remove dead skin. Lactic acid is a very mild acid, and even in yogurt or sour milk, it’s very dilute. If it could seriously remove dead skin, you’d notice some exfoliating effect from spilling yogurt on the dead outer layers of your un-burned skin, which is certainly not the case.
The cool milk is soothing and moisturizing, which is fine, but let’s not roll out the pseud0-science to make it sound like some kind of dermatological breakthrough. Noxzema or any mild lotion would have the same effect.
I use aloe gel, but I make sure to get the 100% pure variety – many of them contain alcohol or other crap that makes sunburns worse.