If you have php running, you could use phpMyAdmin to create and manage MySql databases. If you are using a web host that is supplying you with a MySql database and php, then there is a high degree of certainty that phpMyAdmin will also be available for your use. See http://www.phpmyadmin.net. Set up is not the most intuitive.
Another product to look at is MySql Control Center which is available at www.mysql.com. This product allows you to create databases, tables, etc.
One problem you will have is getting data out of the Access table and into the MySql tables without writing a program. If your MySql database is local to the Access database, then install the MySql ODBC driver (also at www.mysql.com). Then you can use the link tables feature of Access to tie the MySql tables into the Access database. From there, you can load the tables using Access routines.