Also, there can be a big difference using one laptop vs. another. So some models might cause you this symptom, while others may not. Unfortunately, it's pretty difficult (or impossible) to predict what a sensitive person is going to react to.
Also, using the laptop on battery power (not actively charging) might help.
I have a Chicony KB-0005 that I bought for $10, and it solved the burning problem. Its receiver uses an old PS/2 port, so I use an adapter to connect it to USB.
One thing to be careful of: Some of the IBM and Fujitsu infrared keyboards may not come with an external receiver. (I think they used the built-in infrared receiver on the old computers they were designed to work with, so they probably won't work with other systems.)
Edit: It also has a built-in track button, so you don't absolutely need a mouse.