If you don't mind a bit of manual work you can add constraints to your label using a SpringLayout. This allows you to position edges an exact distance from other edges, which by default also sorts the components size (By basically setting the edges a set distance apart when you lay it out) I have demonstrated below with a textArea, but is could easily apply to your label as well.
public class SO {
public static void main(String[] args) {
//Components
JFrame frame = new JFrame();
JPanel panel = new JPanel();
panel.setSize(frame.getSize());
JTextArea text = new JTextArea();
//Add components
panel.add(text);
frame.add(panel);
//Layout add & setup
SpringLayout layout = new SpringLayout();
panel.setLayout(layout);
layout.putConstraint(SpringLayout.WEST, text, 10, SpringLayout.WEST, panel);
layout.putConstraint(SpringLayout.NORTH, text, 10, SpringLayout.NORTH, panel);
layout.putConstraint(SpringLayout.EAST, text, -10, SpringLayout.EAST, panel);
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
frame.setLocationRelativeTo(null);
frame.pack();
frame.setVisible(true);
}
}