Sherlock 'deduced' that he must have had a root canal - that is a procedure that would have had Mycroft in pain for a long time. They weren't saying he was at the dentist, but that he'd been to the dentist. Later when we see Mycroft in person, he does indicate pain in his jaw when speaking.

Not to rain on anyone's parade, but I've had two root canals, and I was never in such pain that I couldn't or didn't want to talk. And the procedure itself doesn't usually take more than half an hour, maybe an hour if there's complications.

Obviously everyone is different, but with me, the most pain I had was before I went to the dentist. While it's certainly not pleasant to be poked with a metal stick up your root canal, anything that the dentist did only helped to relieve the previous discomfort I had. While of course it's not impossible that Mycroft had a very painful experience, he must have had one hell of an infection to have his will to speak impaired for hours on end.