It is possible for some game data on the SD Card to be corrupt while other data is just fine.  I suggest that you get another SD Card and use that to redownload your games.  You can also redownload directly to the system memory.

You could probably try deleting the game data by putting the SD card into a computer and if that doesn't work, just formatting it from the computer. I don't think 3DS supports downloading eShop games to the internal memory (unless they are DSiWare.) This page (click here) has formatting instructions if you try that.

I think there is a Nintendo 3DS folder that would contain the games. I would check to see if it's obvious which folder contains the games.

If you do try a new card, this page (click here) explains how to copy data over.

If you get some kind of error message when you try to copy the games folder, there might be some corruption and it may require formatting the memory card. I would try just deleting the games if you can to see if it will let you do that much. Otherwise I'm not sure there's much you can do.