No need to worry. Update (or re-installation) won't affect the database or your server. Until the plugin is activated, you won't see your data (for example, galleries).
It seems that Wordpress does not have sufficient permissions in order to install the plugin. It is necessary to remove the plugin folder via FTP and install the plugin once again.
Follow the next steps in order to delete (remove) Wordpress plugin manually via FTP:
- Download and install FTP client (for example, Filezilla).
- Open FTP client and enter your FTP access credentials (host, username, and password) to access files on your server.
- Navigate to 'yourwordpresswebsite/wp-content/plugins' directory.
- Disable necessary plugin by removing (deleting) its folder.
If the error still appears (plugin installation fail), you should set permissions to 755 for the 'yourwordpresswebsite/wp-content/plugins' directory and try again.
After installation just activate the plugin and everything will be fine.