Question for Dentists/Tooth experts...
An abscess will deliver a kind of pain that you simply can't imagine. Truly. I've had four of them and if I'd had a Derringer for the last one, I would have cheerfully blown my own jaw off, it hurt that much.
You could go for a second opinion, of course. It may be possible that a pulpotomy and new filling will do you fine. If not, get the root canal and crown ASAP.