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Burning mouth can be caused by infectious organisms and certain drugs but you definitely do not have an antidepressant deficiency so that wont cure it but may create additional problems.
Some types of virus are controlled by dmso so that would be a cheap easy way to start and see if it will work for you.
A more severe organism that can be the cause of trouble like this is mycoplasma infection. If doctor prescribed antivirals don't work, if dmso fails to work then try colloidal silver or a big gun virus / mycoplasma killer called gallium nitrate. Certain types of nerve infection are horribly painful until gallium nitrate comes along and nukes the germs responsible. Have a great day.