Yes, it's possible to inject code from URL it that is not properly Sanitized.
Check this link for how to prevent database injection attacks and write secure code.
Always give proper permissions to files for anonymous users.
Upgrade to latest version of Drupal for new security releases (Test it before moving to production)
Look at all the roles on your site. What permissions do they have? Which have advanced permissions that could be used to take over a site? Perhaps there is a new role you know you didn't make. Is there one user with that role? Check fo this.
Plan for the Worst
While no one wants to consider that their site could be vulnerable, you must hope for the best but plan for the worst. This means making frequent backups that you can upload in the event that someone hacks into your Drupal site. Backup and Migrate is one such module that allows you to schedule backups and import saved databases.
See this link for more info on "Remote Code Execution"