go to Android/data/com.gamesas.falloutshelter/files and check if there are files there that arenamed vaultX.sav (vault1.sav is for the first slot). If they're there, check if the're 0KB or more. If they're at 0KB, I'm sorry, but your game is as good as gone. You can try to recove it using DataRecovery software, but I doubt you'll get anything knowing how flash memory works.
If your files are more then 0KB, then you;re in luck. Copy the files somewhere to have a backup and then try to reinstll the application, and after you do copy the files back into the 'files' directory and check if they load. worked for me, shem it wasn't the vault I wanted to recover...