Your webhost has probably restricted the access to your database so that only a specific host can connect to it, namely the one hosting your PHP based website. This is a common practice.
If this is the case, you cannot connect from any other host - and thus, your C# winforms app won't be able to connect either.
So a direct connection from your C# app to your database isn't an option, but you might implement a REST interface with PHP that serves the data you need to the outside world. This could then be accessed by the clients using your C# app. This is the only solution I can think of.