I doubt you damaged anything since the offending piece was brass!
Actually, if anything was damaged, I suspect it was from the steel (presumably) cleaning rod. Still, it wasn’t like you could just leave the stuck piece in your chamber – you did what you had to do!
Suggest you clean the chamber and then look straight into it from the rear with a flashlight to see if you see any damage.
If you don’t see any problems, then take the rifle out and shoot a few rounds. If it cycles OK then you shouldn’t have a problem. You might also want to look at the ejected brass for any strange marks.
You are definitely not the first person to ever get something stuck in an AR chamber!! [:D]
I’d be very surprised if any damage has occurred.
Edited to add that if you have some serious accuracy problems, that could be from a damaged throat. I still don’t think it’s likely, though.