Hello. Please do not, do not, do NOT tell them. What you're describing to me is very similar to my mom about 5 years ago (in more ways than one). She, too, was doing several people's jobs in her one position. She was heavily relied upon, her hands were hurting her so bad (to the point where she couldn't even open up her oldest grandchild's sippy cup, jars, grip the steering wheel, etc.). Like you, she ended up doing a workman's comp claim, and the doctor actually DIDN'T diagnose it with carpal tunnel (which is what we were all expecting). She was told to begin taking 1 alieve a day to help with the inflammation. Now, I would say that this was a crock, because the company you work for usually can choose which doctor you have to see, BUT she was able to change jobs within a year of the appointment, and here she is about 5 years later and her hands are fine....great...as in little to no problems at all. She has no problems with sippy cups, driving, opening jars, etc. now.
I also know from her experience with the job hunt that it is really tough to find a job in this economy. People didn't care that she was loyal to her previous position for 30 years (she was 50 when she switched jobs). She is happily in a new position now and has been for a few years, but it took a while to get there.
NEVER give your boss advance notice that you are looking for a new job...every person is expendable (sorry...that is sad to say). Plus, you can go from being the favorite to the hated in a short while once you are no longer 'theirs.' Find another job first. Make sure it is secured. THEN let your boss know. :)