Burning sensation on your lips can be due to-
Intake of spicy ,sour,allergic food stuffs.
Oral habits like tobacco or pan chewing.
I would advice you to get a thorough clinical evaluation by a dentist
Apply dologel on the affected areas.
Rinse your mouth using warm saline frequently.
Take nutritious rich food as well as plenty of fluids.
Avoid spicy foods.
Take vitamin becosules
Get your decayed teeth restored or extracted .
Meanwhile,visit a GP too.