I am experiencing mouth pain (quality: stinging or burning sensation), difficulty swallowing, gum swelling, spots on roof of mouth and around sides?

Burning Mouth. Burning mouth syndrome? A possibility if other causes (infection, allergy, burns) have been ruled out. See your physician and/or oral surgeon to be examined and treated. http://www.mayoclinic.org/diseases-conditions/burning-mouth-syndrome/symptoms-causes/dxc-20179960.
Diagnosis ? These types of situations require a complete medical and dental history along with a complete and thorough clinical examination. There is a host of possible causes which can only be determined and treated by a one on one visit to your dentist. The cause may be dental, medical or a combination of both. Make an appointment.