I've never had problems with my thumb (with Luigi, but Fox tech tends to tire it out), but have sprained my right middle finger from hitting the R button to wavedash (taking the spring out of the trigger really helped with this, especially on white controllers which have stiffer triggers). You may just be more susceptible to this kind of thing than most people, which is unfortunate. I would recommend seeing a doctor if this happens a lot and getting their advice. Also you might find this guide useful:
http://smashboards.com/threads/staying-healthy-a-guide-to-playing-melee-better-and-longer.332355/
Do you hold/use the controller in an unusual way, or is there something different about your controller that could lead to what you've described (damaged button, etc.)? Do you do any other activities that would also wear on your hands significantly (such as playing guitar)?
Since you're describing blistering on your thumb I'm not so sure my advice will apply, but stretching my hands seriously helped me (and even if it doesn't help you so much with your specific problem it will increase the effective lifespan of your hands in general). However, the advice of taking breaks from practicing techskill definitely does apply; seriously, in the long term it gives you back more than you lose from spending slightly less time practicing, and of course the time spent in between sessions resting your hands doesn't have to be entirely wasted. In fact it can be spent completely productively, or on more Smash practice even (in the form of analysing videos and things like that).
I should probably mention that I use the X button to wavedash, sliding my thumb off the right side of it.