I've had a lot of teeth extracted over the years, but never for a broken tooth (about half a dozen "deciduous" teeth that were too stubborn to make way for the "permanent" ones*, and five [yes, five] wisdom teeth, all of which were completely impacted and had to be chiseled out in two separate batches [I opted for general anesthesia on both occasions]). The worst of them was the second round of wisdom teeth (the final three). Due to a nearly lawsuit-worthy mishandling of my recovery from the anesthesia, I had torn the stitches out before I reached home. (Don't ask. Really.) In that instance, I was still in pain about five days later (on the day of my marriage to my first wife). The other extractions settled down much more quickly; maybe three or four days for the second worst (the first round of wisdom teeth).

I said all that to say this: you have my understanding and sympathy, as well as my best wishes for a speedy recovery.

And good luck with the bike.

*I still have a primary molar where a bicuspid should be; said bicuspid is believed to have manifested as wisdom tooth number 5.