For 1 week: mild jaw pain, swollen 'coated' tongue, canker sore underneath tooth on tongue. doctor thinks reflux. smoker. should i get second opinion?

Your symptoms: If you feel it necessary. Stop smoking and see a gastroenterologist for testing to confirm or negate that diagnosis.

Smoker: As you are a smoker, and smoking (anything) causes oral cancer, I would want a second opinion from a specialist Oral Surgeon or a specialist Oral Pathologist. And if you are suspected of having Reflux, evaluation by a Gastroenterologist is also strongly recommended.