Your pivot shoe looks to be fairly old, but we may still have a match. Before I can suggest anything, though, I'll need measurements.
To start, please remove the shoe from the window and measure its width and thickness. Then, write them down and let me know what you get. I'd also like to see a photo of the shoe removed, while you have it out.
If possible, I'd also like to see the pivot bar. No need to remove it, I just need to see the tip. I want to ensure that any shoe we recommend will be compatible with it.
If you're only repairing one window, I wouldn't suggest getting the jamb spreading tool. That's a very expensive investment for a very quick project. It would be easier (and cheaper) to make a cutout in the jamb so that you can remove the shoe. That's only assuming that no such cutout exists to begin with, of course. Make sure to check under your sash stops just to be sure.
Making a cutout in the jamb to remove the shoe is very simple and would allow you to verify size before you buy anything. I'll share a video guide on how this is done, which you can see below. If you can't verify size, you're stuck with a lot of trial and error that will end up being more work in the end. Better to take the shoe out twice, to measure and replace, rather than multiple times due to erroneous purchases. You're not going to know for sure what shoe you need until you measure it.
No problem! Please feel free to reach out if we can be of any further assistance.
