From what you have written and tried... It sounds like there maybe damage or a fault to your SD card reader. Regardless, I would back up my phone data and do a hard reset... Then restore my data then try again. If the issue persists then I would go down the manufacturer warranty route, it would be handy if you're able to get to a Samsung Experience store nearby. If not, and you got your phone from your network provider, then you can check your warranty options with them. If it's purchased by another retailer then you may need to contact them too.
