In this blog post, I will explain the cures for both spicines and brainfreeze. I hope this saves a culinary life :).
Brainfreeze
When you get brainfreeze, thrust your tongue against the roof of your mouth. When a very cold substance touches the roof of the mouth, the blood vessels in the brain dilate, causing a headache. By pressing your tongue against the roof of your mouth, you are warming the area, causing the blood vessels to contract again.
Spiciness
We're going to have to go into the molecular level for this one. The substance that causes spiciness is capsaicin. Capsaicin isn't water soluble, so water type liquids such as soda, iced tea, and, of course, water will do nothing. Actually, it will do something: spread it around. Not to fear, though: capsaicin is milk soluble. drinking milk will cure it pretty much instantly.