How about a bucket of ice and a bottle of Jack Daniels?  Repeat if needed.

With your palms forward is the pain on the outside ????   The brace you have is an effective one it works by relieving stress on the tendon.  The reason wrist motion often hurts it up there is that the muscle that is involved inserts down at the wrist.   Ice the area, stay on the NSAIDS, possible cortisone shots.
Strengthening the muscles can help.  Here are the ones I would give
     Forearm extensor stretch. Raise your affected arm out in front of you 90 degrees, in line with your shoulder.  Turn your hand so that your thumb is pointing down towards the floor.  Bend your wrist, and with your unaffected hand, grab your fingers and bend them back towards you to increase the stretch in your forearm.  Hold for 15 seconds and repeat for 10-15 repetitions, 3 times a day.
 
You can also try a prayer stretch wherein you position your hands and arms as if you are praying, keeping your hands together while moving your hands up and down in front of your body.
 
 
Strength training. This can help heal your arms and prevent further injury. Place your arm on a bench and use a light weight(full water bottle works well). Curl your wrist and bring it towards you. Do this 10 to 15 times every day. Do more sets as the pain subsides.
 
 
Flexibility exercises. Put your arm on the table with the palm up. Make the fingers touch each other for about 10 to 20 seconds. You may also do another exercise with your hands forming a fist. Twist your wrist slowly and stretch it hard. You can also try the palm flipping exercise on a table and do it 20 times.
Squeezing techniques can be very helpful.  For this you will need something similar to a stress or tennis ball which you can squeeze.  Simply squeeze and hold for 3 seconds and then release.  Do this 10 times in a row every day. This squeezing technique will help to strengthen your injured
 
Avoid activities  stress that muscle like swinging a hammer.

Thanks Clint.
As I said this has been an off and on struggle for a decade.
I do those exercises when the pain occurs but when I am not over stressing it and the pain stops I get lazy and stop.
Til next time.
Yes ice, NSAIDS,exercise and rest.
Well 3 outta 4 ain't bad.
I'll stop whining now, I promise.
 
 
I lost those fish because I suck and my hooks were too small.
 

That's not good!  I've got all sorts of pains, but nothing real major yet. It's the reason I got the new switch. My wrists and right elbow  are starting to be problematical.  Another chaser of carp, eh? At least they don't require repetitive casting and I generally use a 6 wt. or less.  They do require
a whole lot of strain to land.  And in your case, the quick reaction hook set has to be painful. Geez, we'll have to share some tricks. I've been chasing them a long time. I started with doughballs when I was pre-kindergarden, but have sight fished them with flies off and on  since I was a teen. The past 15 years- ON.   I have to be very quiet about my  carp haunts now, I mistakenly told one friend about a favorite flat, and now it gets flailed by guides and wannabees. HT has some good water  near him, too. Oh yeah, he lives on the Delaware I have fished for them around the country and have landed some in 10 different states.   Yeah,  not using  1/0's  must have contributed to the problem, no doubt . That and lack of experience.  Oh yeah, and your too short.
 

Carp can be tough sobs.
Had a place near some wheat silos that when the trucks rolled in wheel barrels full worth of grain heads would miss the chute.
They'r sweep them up and dump them in the water.
Hundreds of carp would chase the grain as it floated with the current taking it off the surface.
They would tip up almost on their backs and inhale it from an inch under the surface.
I had them suck the fly under but reject it before it got to their mouthy when it caused drag on the tippet.
A perfect drag free drift was required with enough slack left at the end to negate that.
 
Local TU took a survey years ago asking what people did when it got to warm to fish trout and when I wrote carp fish they made fun poof me in the newsletter.
5 years later the had to all but take a ticket and stand in line to carp fish.
I've caught some in LO that you could literally put your fist in their mouth.
Took more line than any king I have ever hooked.
 
Merry Christmas to you 
 

I have a friend who is a SERIOUS carp fisher.. He has landed some well over 50lbs, locally as well as on the Ct river .. Maybe I'll post up some of his catches.. I'm sure Charlie would be quizzing me though if I did..lol 
He kinda got me interested in them again but really I just go out back and fish them for chits and giggles..

I was scouting a small trib in early may a bunch of years back and saw a carp in there that had to of been twenty pounds. At first I thought it was a monster steelie. Saw a few steelies the carp and a small mouth that day. What an awesome fishery.

I usually always tried to avoid carp while targetting other species. A pond I grew up near used to have monsters that wed catch on corn under bobbers in the fall. I can see how tar getting them with a fly can be fun. I've heard berries attract them. I suppose a glo bug would work well in different colors. Maybe even white.

hen L13 was an Orvis shop rat there was a mulberry bush that overhung some carp water.
Purple deer hair flies were nice to have if you were going to "try a rod out"
 
My top water was spun hair to look like whrat heads or later white CDC feather with a brown deer hair sot to imitate cotton wood fluff.
 
O cheese or white glo bugs were a sure thing for the bottom feeders in the wheat dump zone.
Mostly 8-12 pounders with a few reaching past 20.
 
The big boys in LO were at night fishing alwive or smelt streamers for salmonids.

2B-
 
It is a royal Pain to get used to, but you could try becoming a southpaw.
 
I work at it when I get fatigued, kind of like counting steps in case you go blind!
 
L13  

Ya L I lost one to a weenie set lefty the other day.
I just doubt myself fishing that way.
Also in that back eddy it pays to set upstream and down current and lefty I just react against the pull.
I do it a lot at the SR but have more line out that lets me deley the hook set while it draws the hook into the mandible.
In the elavater it is so close up I just don't get a good feel for what's going on lefty.
 
Oh by the way  you should go as soon as you can.
All my takes were on red- orange ostrich flies with a bunch of copper flashabou.
Maybe 18 inches of vis that day much more now I bet.
And that was part of my problem.
The takes were so hard it hurt before I did the hook set.
Kind of timid.