When an ear, nose and throat doctor confirmed that I had tonsil cancer in October 2016, it came as something of a relief. I know that probably sounds strange. But compared to the other types of cancers I’d been worried I might have, this one didn’t seem so bad.

My doctor told me the tumor he’d found wasn’t very big and was clearly visible through a scope. He also said it was in an easily accessible location, so it should be fairly...