You should probably go back to the doctor that gave you the first class medical and make sure this isn't a problem before you spend any more money on flying.
10 hours of flying and you haven't landed yet? That's a huge red flag. I'd be looking for a new instructor. I usually did the landing on the first lesson then had the student working on them on lesson 2 and beyond. I haven't instructed in over 10 years, so hopefully someone more up to date on recent training trends can chime in but this sounds unreasonable.
I can't speak to your specific condition but I've met two pilots that both had essentially no use of one hand. One was a CFI, the other an airline pilot. You need to get this addressed though. I'd start with AOPA aeromedical.