Cannot achieve my server

I've been using HeidiSQL for a long time, both on local server and on remote server with no problema.
But i've recently changed my webhosting, so I changed all the connections in order to redirect to the new server with new credentials.
But none of them Works. When I create a new connection with the new IP Address (i.e. X.X.X.X I get always the same error:
SQL Error 1045 Access denied for user user@Y.Y.Y.Y. Where Y.Y.Y.Y is my public IP address and not X.X.X.X which is the server IP address I've configured.
Does anyone knows where is the problem?
Thanks in advance.

Your new host accepts external connections (thus you're able to receive an error message) but the user you have (or think you have) either does not exist or has a different password than the one you're trying.

You must remember that in MySQL Server you can have identical user names with a different suffix, e.g:

jim@localhost
jim@192.168.1.100
jim@%

The suffix determines whether you're allowed to connect from a given machine.

I'm not sure this could be the problem, because with another applications (MySQLWorkbench) I can connect with no problems.

Not being able to see your full Workbench and HeidiSQL inputs, I still suspect wrong credentials.

(And you're somehow expecting to see the server IP address in the error message, which suggests you might not be aware of how MySQL permissions work.)