When you have General Anesthesia you are usually “intubated”, that means a tube is placed down your throat through your vocal cords and into your lungs. This is what keeps you breathing while you are sedated.
There are many reasons you can have a sore throat after being intubated; it may have been hard for your anesthesiologist to place the tube and soft tissue trauma occurred, you may have a sore throat just from the position of the tube or depending on the type of surgery you had manipulation of the tube may have irritated the tissue in your throat.
If you are intubated for having your wisdom teeth out (sometimes it is just done under heavy sedation) the tube will often undergo a great deal of manipulation as the teeth are removed bruising the tissue. If you were not intubated it may just be the position you were in and laying with your mouth open has irritated the tissue.
It can be very painful but it will go away. Topical remedies like Cepacol spray can help (or the lozenges suggested above), drinking ice water can help reduce the inflammation as well.
Hope you feel better fast!