DM,
I am an oral cancer survivor and a dental hygienist whose initial diagnosis was made with a brush biopsy. Your dentist is 100% right to be aggressive about checking things out because that is the only way oral cancer is found early. But to put your mind at ease, 85% of brush biopsy results come back as normal. Of the results that come back as "atypical" and need a scalpel biopsy, only 30% of those are preancerous or cancerous. The white patches under your tongue are most likely okay, but if you continue to smoke, and the white patches remain, you should have them brush biopsied annually. Just because they are okay today doesn't mean they can't under go a malignant change in the future. If you quit smoking, most of the white patches will go away within a few weeks. Any that remain should be removed because they are the spots that will most likely become precancerous or cancerous.
Please let me know what happens with the brush biopsy.
Barb