Is it normal to have mouth pain while wisdom teeth are coming in?

Yes, somewhat.: This can be common, especially if they are tight. If this persists, you might have to go back to your dentist and/or see your doctor to make sure it is not something worse, like infection.

See your dentist.: When your wisdom teeth are erupting they often cause an operculitis, or infection of the operculum, which is the tissue "window" covering the partially erupted tooth. You may notice swelling of your gum tissue in the third molar area. Pain can also occur from horizontal impactions from the third molar, "wisdom tooth", or the second molar from the pressure caused on the root.

Yes, but: Yes, but at your age, will never completely come in and will likely cause problems. Best thing is to see the wisdom tooth expert. For best results with wisdom teeth, make sure you are evaluated and treated by a board certified oral & maxillofacial surgeon.