I suggest you start with the most common, least alarming possibilities here.
Any chance something is caught in your gum back there? Or next to an adjacent tooth? My gums sometimes get inflamed after I eat popcorn - until I pull a lingering husk out of them. If you haven't yet, you might use some dental floss or a toothpick to see if you can find anything. I wouldn't go digging in the extraction site, just around it and around the adjacent teeth. Do you see any swelling?
If you don't find anything, you might push on the adjacent tooth a little with your tongue or something to see if that is the source of the problem rather than the empty socket. If that feels abnormal, you should get it checked. If it doesn't but you still lack an explanation, you should get it checked.
One thing that might help until you figure out what is wrong is changing the temperature of your drinks. You might find that a different one doesn't have the same effect - and if it does, at least you'll know. You would have hurt if you hadn't, anyway ...