Otherwise most wrist injuries gradually improve with time and benefit from partial rest. A non-compression wrap or splint is helpful if it enforces partial rest.
In the first 1-3 days, a compression wrap may be helpful to limit swelling. There is no other benefit from compression and after 2-3 days there is absolutely no benefit at all from compression.
Pain that has not been improving and completely resolved by two weeks after injury needs evaluation by your primary care physician.