"I've had all four wisdom teeth removed this morning. On my way home, I couldn't stop sneezing and my nose won't stop running. I still can't stop my nose from running and I'm sneezing periodically now. I'm concerned I have dry socket. The AC was running so I might have also gotten cold during the procedure. What should I do?"
What you've mentioned here may warrant some cause for concern. The sneezing is not good in itself as it can cause a dry socket. Dry socket appears later, a few days later in fact, so it's likely something else. But "why the sneezing" is the more important concern.
I'm suspecting that this is a result of the surgery. An allergy to latex, or an upper wisdom taken out that has left a hole between the sinus and mouth can irritate the sinus and make you sneeze.
My advice is to get it checked out right away. Have your dentist observe the upper sockets while you blow your nose and listen for a gurgling sound. While there are other possibilities (you could have suddenly gotten a cold while in the chair, but as you mentioned), that sounds unlikely. In the meantime, covering the socket with gauze or a tea bag while you sneeze is a good idea.
Dr. Mark Burhenne