The white led on your loupe is probably blue light with phosphor. Although it's not in UV range, it may sting your eyes a bit (the same reason why you shouldn't stare at the curing light). Try putting on the orange filter (aka composite filter) and see if it makes a difference. It should block these wavelengths. Also, vitamin A supplements can help with eye strain, and from my experience, coenzyme q10 works well too.
Personally, I was more concerned about flourescent lightings in my school and got a pair of transition lenses to block low-level UV rays emitted from them. Maybe you can ask your loupe company if there is an option to use transition lenses.