Java mysql db testing with testContainers and Docker

I want to use testContainers because, from what I understood, it is a container of the database at some point in time ( we can pull that database state with Docker, so no mocking and stuff). Then we can just test it ( insert some stuff, assert that it is in the db, delete it, assert that it is gone, etc.. ). My problem is that I can't pull the image of the database with Docker. Moreover, the database is remote ( hosted by my university ). It has username and password. If someone can help me with getting the image and injecting it into MySQLContainer (https://www.testcontainers.org/modules/databases/), I would be really grateful. Here is my code:

public class SQLConnection {

    protected transient Connection connection;
    protected transient PreparedStatement preparedStatement;
    protected transient ResultSet resultSet;
    protected transient Statement statement;
    protected transient String url = "jdbc:mysql://remote.host.nl:3306/project_Name?useUnicode=true&useJDBCCompliantTimezoneShift=true&useLegacyDatetimeCode=false&serverTimezone=UTC";

    public SQLConnection() throws SQLException {
        try {
            Class.forName("com.mysql.cj.jdbc.Driver");
            Properties connectionProps = new Properties();
            connectionProps.put("user", "remoteDbUsername");
            connectionProps.put("password", "remoteDbPassword");
            this.connection = DriverManager.getConnection(url, connectionProps);
        } catch (Exception e) {
            System.out.println(e.getMessage());
        }
        this.statement = connection.createStatement();
    }

    public void closeSQLConnection() throws SQLException {
        this.connection.close();
    }


    public boolean DBRegister(User user) {
        try {

            String query = "INSERT INTO `user` (`username`,`password`,`email`, `high_score`) VALUES (?,?,?,?)";
            this.preparedStatement = this.connection.prepareStatement(query);
            this.preparedStatement.setString(1, user.getUsername());
            this.preparedStatement.setString(2, this.hashPassword(user.getPassword()));
            this.preparedStatement.setString(3, user.getEmail());
            this.preparedStatement.setInt(4, user.getScore());
            this.preparedStatement.executeUpdate();
            System.out.println("Registration worked for user " + user.getUsername());
            return true;
        } catch (Exception e) {
            System.out.println("Username already exists :(");
        }
        return false;
    }

    public boolean DBLogin(User user) throws Exception {
        try {
            System.out.println(user.getUsername());
            String query = "SELECT * FROM `user`  WHERE `username` = '"
                    + user.getUsername() + "'";
            this.preparedStatement = this.connection.prepareStatement(query);
            this.resultSet = this.preparedStatement.executeQuery();
            this.resultSet.next();
            String storedPassHashed = this.resultSet.getString("password");
            return this.checkPass(user.getPassword(), storedPassHashed);

        } catch (SQLException e) {
            e.printStackTrace();
            System.out.println("User does not exist");
        }
        return false;
    }

    private String hashPassword(String plainTextPass) {
        return BCrypt.hashpw(plainTextPass, BCrypt.gensalt());
    }

    private boolean checkPass(String plainTextPassword, String hashedPassword) {
        return BCrypt.checkpw(plainTextPassword, hashedPassword);
    }
}