From the description you've given, especially the part about the camera failing to format the card, it sounds like there's just simply something wrong with your SD card, so that probably means throw it out and buy a new one. They aren't that expensive these days.
Even if you can get the card to work again, it's not worth continuing to use a card that you already suspect has problems.
It's a fact of life that some SD cards fail at random times, and sometimes this means they'll fail when they're quite new. Count yourself lucky that you haven't lost a bunch of irreplaceable photographs that were on it.
Before you throw it in the trash, however, a few simple troubleshooting steps:
Try another SD card in the same device. Same problem? Then it's probably the device, not the card.
Try the problem SD card in a different device. Any problems? Then it's probably the card.
Check for dust/dirt/fluff in the SD card slot of the device (camera) and on the SD card's contacts (avoid cleaning them unnecessarily especially with dry fabric, as static electricity is harmful to them).