Is it normal to feel a sharp pain when a healing cut on my knee rubs against the fabric or is exposed to pressure? The cut is from falling on the sidewalk and scraping my knee against the rough pavement. Does the pain indicate that my cut is infected

Knee injury. It will be helpful to see the injury to determine if it is infected or not. If the area is red, swollen, painful and warm to touch then that may suggest infection.
You most likely. damaged some superficial (tiny) NERVES when you fell! This has resulted in what is called "hyperesthesia" and will subside as the nerves heal...(they take longer to heal than your skin (weeks-months) but eventually they will heal or "die" leaving you with an area of numbness!

My Opinion only but I hope it's helpful
Dr Z.