Hosting companies really don't like to make their MySQL servers accessible from the whole internet. You share that server with other customers, and it's pretty easy for cybercriminals to crack, or to do a denial-of-service attack, on MySQL if they can get to it. Considered harmful.
Some hosting companies, including yours, make an exception so you can whitelist one or a few particular IP addresses for remote connection to MySQL via the net. Apparently that solution is not workable for you.
But, they would be insane to allow access from the whole internet. If you owned the MySQL server (or the Oracle, postgreSQL, MS SQL Server or DB2 server) you too would be insane to allow access from the whole internet.
Desktop applications which access remote databases over the public internet are vanishingly rare, for precisely this reason of security. That sort of approach to application development is much more commonly deployed inside corporate firewalls.
It looks like development of a webservice is in your future if you must deploy a desktop app. The good news is there are many good and secure ways to do that.
Dotnet provides a good, if complex, infrastructure for webservice development in their WCF (Windows Communication Foundation) subsystem. A webservice is basically a web site that's designed to be accessed by programs rather than by humans via browsers. The two generic terms for webservice architectures are REST and SOAP.
Desktop programs (like online games) that use network resources usually are set up as clients of one or more webservices.