I am lucky to be in good health, but had similar issues with my right thumb on starting up again this year. Let's be honest - the ergonomics of the sax are pretty bad, especially the right hand. The natural position for the thumb is where the F# trill key is. The solution I found was to get a WAW thumbrest:
https://www.shapeways.com/product/F8JVGKSNS/the-deluxe-waw-modified-thumb-rest-for-saxophone
It allows you to place your thumb over the F#. I also tend to rest my sax on my body whether sitting or standing (the Eb guard rests on my waist when standing). It's not textbook, but after having enough pain to have to stop playing for a week I don't really care. It also had the bonus of giving me a position where the right hand palm keys are easier to use. The ideal ergonomics would probably require a redesign of the instrument, as the right hand is more pushing than holding up and ideally this would be done with the palm (the neck strap carries most of the weight and serves as a fulcrum). Unfortunately, we're stuck with what we got.
Another option is to get a stand and play it on the stand. Some stands are better than others but I've seen people use these in performance due to health issues.
Beyond that, if you're having problems with your left hand too, that may be due to the palm keys? You can get pads for palm keys that bring them closer to your hand. Ideally the movements for the palm keys should be small, your hands should be close to them already. When I started taking lessons again, the first thing my teacher did was advise me to bring my left hand down so that it was closer to the palm keys.
Good luck! I hope some of this is helpful.
https://www.shapeways.com/product/F8JVGKSNS/the-deluxe-waw-modified-thumb-rest-for-saxophone
It allows you to place your thumb over the F#. I also tend to rest my sax on my body whether sitting or standing (the Eb guard rests on my waist when standing). It's not textbook, but after having enough pain to have to stop playing for a week I don't really care. It also had the bonus of giving me a position where the right hand palm keys are easier to use. The ideal ergonomics would probably require a redesign of the instrument, as the right hand is more pushing than holding up and ideally this would be done with the palm (the neck strap carries most of the weight and serves as a fulcrum). Unfortunately, we're stuck with what we got.
Another option is to get a stand and play it on the stand. Some stands are better than others but I've seen people use these in performance due to health issues.
Beyond that, if you're having problems with your left hand too, that may be due to the palm keys? You can get pads for palm keys that bring them closer to your hand. Ideally the movements for the palm keys should be small, your hands should be close to them already. When I started taking lessons again, the first thing my teacher did was advise me to bring my left hand down so that it was closer to the palm keys.
Good luck! I hope some of this is helpful.