RSI refers to Repetitive Stress Injury. You see the word 'repetitive' there? So, it has to come with anything that you repeatedly do. No matter wrist, ankle, elbow, knee!
But then, if you think a bit more, the strength we have in our extremities is different from each other. Said that, by nature, legs are stronger than hands. Extending this further, toes ...
Go see an orthopedic surgeon; it's not exactly the most classical story but you might have some form of carpal tunnel syndrome. In most cases in can be effectively treated with rest, painkillers and stretching/exercise (so you don't get unnecessarily scared about the "surgeon" part); either way, considering it's your profession, I definitely think it is ...
I actually did a study on this (pains relation to posture) providing ergonomic assessments and follow ups for office workers.
Ideally you'd look something like this:
They have carpal tunnel wrist guards that I'm sure you'd love to wear.
I'd sit on a Swiss Ball -- doubt this is ...
When you have a laptop on your thighs and you type, the wrists are bent upwards (forcedly) more than when you have a laptop on the table (higher).
Also, arms bent forward and without support can pose a lot of burden on the upper back muscles.
Some sort of table (even portable) can help.