Welcome to health care magic!
On reading your question I can suggest you from my experience that in such cases of wrist injuries
one should go to a doctor, preffrably an orthopedician and get it checked (even though there is no swelling), as we use our hands for almost all our works! There is no pain when you don't move this wrist does not rule out injury
as it is immobilization which is helping you.
It does not appear to be badly hurt but you still you have pain while taking support from that hand.
Had I been at your place I would at least use a crepe bandage or wrist band to keep it stable. You should take some anti inflammatory medicine to help it heal fast. Avoid using that hand, espically weight bearing for some days.
An X- Ray wrist and hand will make the picture more clear.
hope this helps you in your problem. Feel free to ask any more question on this.
Dr. Manisha Gopal