Identifying window replacement parts

I have single hung tilt windows with spiral balances. The house/windows are about 19 years old. I've viewed your videos on identifying the type of balance, but mine do not have colored tips, and the diameter seems between the two options. Diameter seems between 3/8" and 4/8" (see photo). Length is about 29 1/4" to under 29 1/2". I need balances for two windows. I suppose at the same time I could replace shoe/shield or whatever the corresponding parts are. Two windows. Window weight is about 20-22 pounds. On one of the windows, the pivot (or whatever the metal piece is called that comes out from the bottom of the window) is broken off. I need to see about replacement piece for that, and hopefully I can use pliers to pull out the broken piece from the window. I've attached photos. Thank you.