You're smart to get it checked out by a sports medicine specialist.
You were also smart to get it checked out in a timely fashion, and for many that means seeing an ER physician.
I didn't mean to bash ER physicians or your hospital.
ER docs usually have great talent to take care of life threatening emergencies, and at least evaluate problems to decide if they constitute an emergency.
So many of the non-emergency wrist problems they see are "minor" strains and sprains, and most get better with rest, splinting and time.
But as you are a tennis player, it is more important to make sure there is not something "more" going on, so you don't go back to play too early and just have an early recurrence, or worsen the situation.
Believe me, I still really hope this turns out to be something that will get better fairly quickly.
Let us know how you are doing.