White patches on the soft tissues that cannot be rubbed off are likely leukoplakia. There are some other possibilities, but this is the most common. Leukoplakia is most common in smokers, but you didn't indicate if you used tobacco or not. This is not always a precursor to oral cancer, but it is important to have it checked properly, as in some cases it can be one of the precursor tissue changes to a more serious problem.
You have misunderstood your dentist in his/her description. Bilateral buccal mucosa only refers to tissue type and location, that is "the soft tissue on the inside of the cheeks, on both sides". We all have bilateral buccal mucosa.
So the thing now is not to worry until you know more. I know this is difficult, but until someone determines that you have a real problem, try to stay calm. Leukoplakia, lichen planus, or most of the other common possibilities, are not cancer. They just bear watching. Remember when you are at the doctor, that no one can diagnose oral cancer visually. If the oral surgeon feels there is something really suspicious, then a small biopsy will be done to determine what's what. This is the only way anyone can know for sure, and if he suggests it, he may only to be doing it to be absolutely positive that you have nothing to worry about.
