need help! my sheets pill and tear from my cats, what material would be best to fix this?

I’m a noob with bedding. I have sheets from TJMaxx and i have no idea what material they are, but they were cheap. We have 4 cats, and our previous bed sheets (jersey cotton from Target) eventually had massive rips in them. Our new sheets are not ripping, but have massive amounts of pilling and loose threads from their claws. I need some recommendations for strong comfy sheets! Willing to spend a decent amount but hoping for under $100.