I have a method getImage() that needs to rotate an Image, store it in a new variable, then return that new Image. Here is my attempt,          
        
You could just use a Rotated Icon and display the Icon in a JLabel. 
The Rotated Icon is a reusable class so you don't need to worry about about adding the rotation code to every class where you need this functionality.
So, based on the example in this answer, you should be able to devise a rotation method which can rotate a source image by a given number of degrees, for example...
  // Make sure you actually load some image and assign it to this
  // variable, otherwise you will have a NullPointerException to 
  // deal with
  private BufferedImage source;
  public Image rotateBy(double degrees) {
    // The size of the original image
    int w = source.getWidth();
    int h = source.getHeight();
    // The angel of the rotation in radians
    double rads = Math.toRadians(degrees);
    // Some nice math which demonstrates I have no idea what I'm talking about
    // Okay, this calculates the amount of space the image will need in
    // order not be clipped when it's rotated
    double sin = Math.abs(Math.sin(rads));
    double cos = Math.abs(Math.cos(rads));
    int newWidth = (int) Math.floor(w * cos + h * sin);
    int newHeight = (int) Math.floor(h * cos + w * sin);
    // A new image, into which the original can be painted
    BufferedImage rotated = new BufferedImage(newWidth, newHeight, BufferedImage.TYPE_INT_ARGB);
    Graphics2D g2d = rotated.createGraphics();
    // The transformation which will be used to actually rotate the image
    // The translation, actually makes sure that the image is positioned onto
    // the viewable area of the image
    AffineTransform at = new AffineTransform();
    at.translate((newWidth - w) / 2, (newHeight - h) / 2);
    // And we rotate about the center of the image...
    int x = w / 2;
    int y = h / 2;
    at.rotate(rads, x, y);
    g2d.setTransform(at);
    // And we paint the original image onto the new image
    g2d.drawImage(source, 0, 0, null);
    g2d.dispose();
    return rotated;
  }