How to hold a thin grip pen?
Finding the right way to hold your pen might simply not work since your preferred way of holding a pen is incompatible with said pen. I hold pens using the (dynamic) quadropod grip, and, although I think it's relatively easy to switch these grips, I doubt that changing grips will prevent your fingers from getting irritated.
I think the problem might simply be a relatively large difference between the size of the pen and one's fingers or hand. Up to a certain diameter, one's fingers will always touch.
Instead, I suggest to get a 'pen grip':

source
You can find them for pens of any size, and in any kind of size or shape.
You can also fashion them yourself out of foam, wood, hair curlers, by rolling rubber bands around the shaft, and a plethora of other options.
I've once used old kneadable eraser to get a surprisingly comfortable (albeit slightly sweat-inducing) 'pen grip':

Reconstruction. But basically the exact same thing.