I am using PHP and MySQL to make a database connection, the only change is that I am trying to access my remote server from my local computer using my server IP address.
1) Check which interface MySQL listen for connections, local (localhost, 127.0.0.1) or remote (0.0.0.0 or IP address). It's in my.cnf. http://www.cyberciti.biz/tips/how-do-i-enable-remote-access-to-mysql-database-server.html
2) Check does your user have corresponding privileges. User that logs in from localhost can have different priveleges from remote one. For example 'user'@'localhost' and 'user'@'%'