The SSH connections usually works in port 22 so it wont affect database connections in port 3306.
You need to open port 3306(considering you are using defaults) and create a db remote user.
At your .env file set the right configurations
DB_CONNECTION=mysql
DB_HOST=EXTERNAL_IP_FROM_SERVER
DB_PORT=3306
DB_DATABASE=yourremotedb
DB_USERNAME=yourremoteuser
DB_PASSWORD=secret
And at your server, make sure that the port 3306 is opened in router and the db username is created with global access not only local.
You can create the global user with these commands
CREATE USER 'newuser'@'%' IDENTIFIED BY 'password';
GRANT ALL PRIVILEGES ON * . * TO 'newuser'@'%';
You can also try to connect to your datase from command line to check connection before you try at your system
Consider 200.200.200.200 as your external IP
mysql -u your_username -p -h 200.200.200.200