my iPhone 15 cord will not fit in my 2020 car

You need a USB-C Female to USB-A Male adapter. Amazon has them as does Best Buy and the Apple Store.

Make sure the cable or adapter you get carries data. Many of them are charge only. If that’s what you want, it’s fine, but if you want to connect to use CarPlay, you’ll need a data cable.

If your car only supports wired carplay, there are a number of relatively inexpensive adapters available on amazon to let you use carplay wirelessly.

“my iPhone 15 cord will not fit in my 2020 car: I think I need to buy something like a c converter or something like that”

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Hardwiring Phone to Car:

That might work, if you have a port. But look into using CarPlay to avoid all of these cables?: Use CarPlay with your iPhone - Apple Support

Cords do wear out from all the bending. If it were me, I'd just buy a new cord of the correct type. They're relatively cheap, under $10 for a decent one.