Try installing Navicat or something similar and create a connection to your database using your external IP address (which you can find using the instructions in previous posts).
You can download a trial of it here. I think they stopped providing a free/lite version a while back, but the trial should work fine for this testing:
http://www.navicat.com/products/navicat-for-mysql
If you can't get a connection to work using the external address of your server, then there is something wrong with your configuration somewhere. It should work fine if you use the local IP address of your server, if you are running it from the same PC.
Some potential problems/solutions are:
1. You are using the incorrect IP address for connecting. You need to use the external IP address of your network because that is what everything outside of your local network will see your server as.
2. You did not forward port 3306 on your router. If you do not forward this port, your router will not allow the connection from the outside of your network to reach your server. It also would not even know which IP on your LAN to send it to. It is very important that you set your router for forward port 3306 to the local IP of the server your database is running on.
3. Your db account does not have permissions to be accessed from remote connections. As mentioned above, you would need to set your account(s) that you are trying to use from the outside connections (such as from EOC) to be able to be used from that source IP or domain name (such as 69.168.254.244 provided in a previous post). To simplify things, you might try setting it to be able to work from all IPs (using *.*), though you would probably want to limit it to specific IPs after you get it working to prevent potential security issues.
4. If everything else has been done and it still does not work, then you are probably running MySQL on Windows and did not check the box to allow remote connections to your DB when you installed MySQL. That can probably be resolved by changing a setting somewhere, but the only way I have ever done it is by running the MySQL install again and checking that box during the install. It is off by default, so I think a lot of Windows users might run into this issue.
I believe that all of that stuff will be required to setup a connection using Navicat that points to your server as if it was an outside address (using your external IP address).
Once your connection works in Navicat, you should be able to use the exact same settings in EOC and it will work.