Do I have a Broken SD SLOT?

Try to remove the SD card using small tweezers or pliers, anything that can fit and get a good grip on the card, in order to attempt to gently slide it out. If you manage to remove it, it might be difficult to see if any of the contacts are damaged. Also inspect the SD card and ensure that no damage has been done to it before trying to use it again.

With a little bit of luck, the contacts inside the slot will be intact, and you will have no problem sliding in and using SD cards, including the one that is stuck as long as it does not get damaged when removed.