Well, I can give exclusive access to a database, then try if you are able to connect from a remote location. If you can connect, again it must be a problem with the mysql server configuration, your router and or firewall. You tried this with freesql.org in the past.

Have you tried to connect to your mysql database server with a php script from another webhost at remote location? Also, is the ip address you have static or dynamic? Did you setup a (free)domain pointed to your external ip address? What does your host look like in the c-script? For privacy not show real ip here, but to sample:

-> www.myhost.com
-> 192.168.1.11 (intern ip)
-> http://192.168.1.11
-> 213.105.17.33 (extern ip)

Furthermore, your webserver has nothing to do with your mysql database server. Even though people can access your website and load your php scripts, this doesn't mean they should be able to connect to the database too.

The webserver uses port 80 (if not selected another port) and the database server run on port 3306, so even though people can connect to your webserver that doesn't say anything about the sql server. Just let the sql server and the webserver run on localhost and from the router forward the ports 80/3306 for both to the correct system. Also trough php admin you must setup a wildcard '%' in order to allow connections from remote locations.

Maybe you did something wrong during installation or configuration and now only allow access from localhost or the internal ip address of the computer running the mysql server. I made that mistake in the past thinking I setup the ip for the server, but instead I restricted access to it only from that ip address.

Dusty