Can Bactrim (sulfamethoxazole and trimethoprim) DS cause a burning sensation in the mouth? Onset 1 week ago, never experienced before.

Possible . Allergic reaction to bactrim (sulfamethoxazole and trimethoprim) can be manifested as oral symptoms, Stop the medication and speak with your doctor. An alternate antibiotic may be prescribed. .
Possibly. While not a common side effect, it certainly may be one. Ask your doctor about changing to another antibiotic, if you are still on it. If you have completed it, then wait another week or so and see if it goes away. If it doesn't, or if you have any other symptoms still, see your doctor.