Is there a way to watch for schema changes in mySQL?
If you use standard MySQL or Percona Server (not RDS, for example), you will be able to use Percona Audit Plugin. You can configure it to only log ALTER TABLEs, DROP TABLEs, etc, see this page:
https://www.percona.com/doc/percona-server/LATEST/management/audit_log_plugin.html#filtering-by-sql-command-type

MariaDB has its own plugin, with a very similar functionality to filter queries (it allows to only log DDL).