I used to have slightly different but similar issues (which were exacerbated when I played on a heavy triple horn!)...
Several things in combination have solved the problem for me:
(1) Adopting a good playing posture...
There's a good article on left hand position here:
http://www.osmun.com/reference/lefthand.htmFor right hand position, see Farkas and/or other standard texts + Observer's comments above.
I would add that for the right wrist to cope with supporting the horn, the right hand fingers need to be roughly vertical.
It sounds like your right wrist might be rotated anticlockwise from this position?
After finding the right posture, review regularly in practice to avoid forming bad habits.
(2) Getting the right instrument:
Some horn designs have the valve levers too far away from the mouthpiece receiver for the left forearm to be able to become vertical enough to support the horn in a relaxed manner.
Some horn designs have the bell too far away from the mouthpiece receiver, or at too wide an angle with respect to the leadpipe, for the right forearm to be able to adopt a comfortable position.
How heavy is your horn?
There are musical as well as ergonomic advantages in using lighter instruments.
After comparing lots of horns, 2.5 kg seems a good upper limit IMHO.
Quite a few double horns and most triples are heavier than this.
(3) Wrist tendon strengthening exercises - search online or talk to yoga experts.
(4) Analyse other things you do that might also contribute to the problem.
eg: if you work at computers a lot, check the ergonomics of your setup, alternate weekly between left and right handed mice, etc etc.