Logging all changes made to MySQL database
There are several tools available to serve the purpose. Following are my favorites:


SQLYog
DB Ninja


Here SQLYog is paid tool, howover it has only windows version available. If you choose this one then its following features will do the job for you:


Schema and Data Synchronization
Visual Data Compare


If you prefer web based interface then DBNinja is great tool. You can compare two database schema easily and fix the differences. following is the example screenshot from their official page: