Chloe --
My husband was in a similar position almost three years ago. His dentist referred him to an oral surgeon because of a sudden (since his previous dental visit a few months before) appearance of a small patch of leukoplakia on his tongue, in a similar location to yours.
The results of that initial biopsy showed moderate dysplasia, not cancer, but warned of a possible "skip effect," meaning that there could be cancer in a section that was not biopsied. The lab that read the slides does only oral pathology, so it may be that the pathologist saw something that raised his suspicions, but he could not definitively say it was cancer because cancer cells were not on the biopsy specimen.
The oral surgeon referred my husband to a local ENT for an excisional biopsy, which took place a month later. (I don't know why the oral surgeon didn't do one initially -- perhaps because of the location of the leukoplakia or because it was thought that cancer was unlikely.) That pathology report came back showing SCC in situ, with a tiny bit superficially invasive. Margins were close but clear. Once cancer was diagnosed, he had his slides, biopsy reports and surgery notes sent to Johns Hopkins -- a comprehensive cancer center about an hour away -- and was examined by an ENT cancer specialist there.
No further treatment (radiation or chemo or additional surgery) was required or even recommended, and the only day he was out of work was the day of the excisional biopsy, because of the anesthesia. He now gets examined with a VELscope at the dentist every six months and also is checked regularly by the local ENT (who is a former chief resident at Mayo) and the Hopkins cancer specialist. He has had two PET scans that showed nothing untoward. So far, so good, knock on wood.
Keep asking questions as you think of them. The people here are the best.