Carpal Tunnel in horn players has nothing to do with whether you play Bari, Tenor, or Alto...Though straight soprano does present some awkward body mechanics, and a lot of stress on the right thumb and wrist.
Physiologically some people are more prone to nerve compression issues such as carpal tunnel. Some people just have a smaller area for all the tendons and medial nerve to pass through, so the nerve gets compressed. Repetitive motions make this irritation worse. I work in the physical therapy field, and deal with carpal tunnel all the time. As much as my boss likes to see the repeat business, the new thoughts are to have surgery sooner rather than later. There are new techniques that don't even leave a scar, and you are in and out of the office in less than an hour! Full unrestricted use of your hand(s) in one week.
If you wait too long, you risk serious muscle wasting, and you can even lose blood supply to the scaphoid bone (pretty important in thumb mobility). If you wait until that point, they just take out the dead bone, leaving you with a void that used to make-up the thenar eminence...That meaty part that is rock hard muscle and bone when you touch tip of thumb to tip of pinky
Sax players are also prone to develop tendinitis (or tendonitis, correct both ways) in their finger flexors and, or extensors. This of course would be felt more toward the elbow...just move your fingers around and look at your upper forearm, right above where you see all the movement below the skin is where all these small muscles attach. If you see someone playing with a strap on their upper forearm, they likely deal with this frustrating and painful problem.
You can help to avoid these types of repetitive stress injuries by playing in good posture and hand positioning (not too flexed or extended at the wrist). STRETCH!!! I like to stretch 2-3 times during a normal practice session, and between sets on gigs. There are plenty of free resources on-line with good finger and wrist stretches. Just don't be too aggressive because you can tear muscle and tendon fibers, especially in these small muscles. If you do have pain, REST! Don't be afraid to use ice, and plenty of it. Play stress free: loose shoulders, neck, elbows, and especially loose wrists and fingers. Oh, and eat protein because it is good for tissue healing.
I hope some of this is helpful. It is all about being good to your body!