At first, you need to check this SD card on another computer to see whether it is still healthy.
If it can be read normally there, it could be the problem of your computer and back up all card data well. Just find solutions to fix the computer problems.
But, if it can be read there, but also gets some error message and card data is still inaccessible, download data recovery software to see whether your wanted data could be retrieved successfully. There are many similar card data recovery programs can help you deeply scan this card and find your data back, like Recuva, 4Card Recovery, PhotoRec and more.
But, if the card also cannot be read there, you must get some serious card problems. Just ask some professional persons for help, when the card data is really important for you.
Note: In the future, you should never forget to back up important card data again.