Can acid reflux cause white toungue and the roof of mouth to be sore (almost like its going away) and under the toungue to be inflamed?

Possibly: But you could also have a fungal infection in your mouth. Do see a doctor to have this looked at.

Yes: If you have a lot of reflux and it gets up to the mouth, it can cause pain and sloughing of the oral mucosa. Stomach acid is very powerful. Acid reflux must be treated for many reasons. It can be treated with medication. The use of over the counter antacids can reduce acid quickly. Prescription proton pump inhibitors are better in the long run as they inhibit the production of excess acid.