Can I use a cashmere comb on bamboo and cotton sheets to get rid of pills or is there something better?

No matter what new pillow cases I use for the pillow between my feet, the friction creates pills after a few nights. I assume this will go away after a bit as old pillow cases don't do this but to get rid of them, can I use a cashmere comb or are the sheets to fine a material for this? Wirecutter recommends a Naadam Cashmere Comb for finer fabrics over an electric fabric shaver, but no mention of sheets is made.