Depending on the phone you have, you normally have two kinds of user memory in the phone, internal memory storage and SD card storage. If you app is self-contained in internal memory it'll never touch the SD card. If the app trys to save data on the SD card, however, it could be running into that error.
One way to check would be to connect your phone to your PC (assuming you have a PC). IF the connection sets up a drive letter, go to the drive letter and see if you can access it and see the data on it. If it doesn't provide a drive letter, pull down the notification bar on the phone and change the mode of the connection. If it provides you a drive letter but gives you an error accessing the memory on the phone then you likely have a problem with your SD card.
If that's the case I'd suggest pulling the micro SD card, installing it into a SD card adapter, inserting it into a SD card port on your PC, and carefully formatting the SD card with the FAT file system. Once done you can remove the SD card and re-install the micro SD card back into the phone.