Do symptoms like de Quervain's tenosynovitis go away quickly?

With surgery, very . Quickly. With avoidance of inciting activity and splinting and anti inflammmatiries ice pretty quickly but may come back quickly.Common in women w young baby.
Possibly. If you are doing it on your own it can take longer but your doctor can try steroids and medication to speed up the process.
With a shot. A cortisone shot can help symptoms get better quickly. Otherwise, symptoms take a long time.