That really sucks and I know how it is. My wife spilled half a glass of Diet Pepsi on her 13-inch MBP. We were horrified and we hurried and turned it off, turned it upside so the liquid could come out of the keyboard and left it like that for at least three hours to let it drain.
After that, I took off the bottom panel and checked for any moisture inside. I saw a few drops inside near the SuperDrive. Cleaned that up and then left it open for about two hours. Then I got a blow drier and blew cool air in it for a good hour to try and make sure any moisture I couldn't see was gone.
We were scared, but I turned it on after less than 24 hours of the spill. To our relief, it worked great. The only thing that happened is the left side keys make a little more noise now when typing on them, but nothing is sticky or anything since it was diet soda lol.
Good luck on your milk. That sugar, fat and protein would make me nervous and I'd make sure to check inside the MBP as well can cleanup any moisture you spot.