I was dumb enough to do the salt and ice challenge. My friend thinks I may have a minor case of frostbite. I would just like to know how I could get it to stop stinging as bad to get them to calm down.

Yes, it's like frostbite. Keep it cool (with ice in a baggie or washcloth) as often as you can. Spray some cortisone on it but don't cover it with heavy ointment or bandages because your skin needs air. Keep it clean, gently. See a doctor if any skin breaks from blisters and it looks like it might be getting infected. You will have a scar.
Take ibuprofin and Tylenol, perhaps alternating. That's what I do because Tylenol works faster but ibuprofin slightly better and longer. Don't go over the dosage.

If it's black or blistered, please go see a doctor.

This will help for frost-nip or MINOR frostbite: Get some warm water- about 100 deg F. Then stick the affected area in the water. Please make sure the water isn't HOT otherwise it will make things worse. Let it soak for a little bit. Next, dry it off and cover it with a cloth bandage if you have one. Keep the area raised to help with the healing. If it's not too bad, you should feel better pretty quickly.
Also, you might try some Aspirin.

There's a reason why you're not supposed to do these things!

Also as a warning for other stupid things you might do in the future, the cinnamon challenge can actually cause collapsed lungs and death by suffocation.