20 minute Ice Cream Headache

In the category of “Things not to try and do in your lifetime”.

At lunch today I was chewing on some ice from my Diet Coke.  I tried talking at the same time and the ice cube slipped down the back of my throat. I figured rather than trying to choke it back up in a public place and possible take the chance of asphyxiating I would swallow it.

However I think it got lodged in my esophagus.  

Do you know you can get ice cream headaches from ice cubes lodged in your throat? Do you know that these tend to be even more severe than a traditional ice cream headache?  
Do you know it takes between 15-20 minutes for an ice cube lodged in your esophagus to melt?

Ouch