private static final String HOST = "200.45.175.34";
private static final String PORT = 5896;
private static final String DATABASE = "bdremota";
private static final String URL = "jdbc:mysql://" + HOST
                                    + ":" + PORT
                                    + "/" + DATABASE;

try {
    Class.forName("com.mysql.jdbc.Driver");
    Connection conn = DriverManager.getConnection(URL);
} catch(ClassNotFoundException e) {
    // hacer algo
}

public Optional<ImageIcon> readImage(uid) {
    String sql = "SELECT bin_data FROM imagenes WHERE uid = ?";
    try (Connection conn = ConnectionHelper.getConnection();
         PreparedStatement pst = conn.prepareStatement(sql) {
        pst.setString(1, uid); // el uid de la imagen a leer
        ResultSet rs = pst.executeQuery();
        ImageIcon icon = null;
        if(rs.next()) {
            byte[] image = IOUtils.toByteArray(rs.getBinaryStream());
            icon = new ImageIcon(image);
        }
        return Optinal.of(icon);
    } catch(SQLException e) {
        // hacer algo
        return Optional.empty();
    }
}

Optional<ImageIcon> oIcon = Clase.readImage("10383");
// si la imagen existe
if(oIcon.isPresent()) {
    // mostrarla en el JPanel
}

clientSocket = new Socket("localhost", 6002);
outputStream = clientSocket.getOutputStream();
dataOutputStream = new DataOutputStream(outputStream);
inputStream = clientSocket.getInputStream();

// mandamos el uid
dataOutputStream.writeUTF("1458");

// y el servidor nos devuelve la imagen
byte[] bufferSize = new byte[4096];
inputStream.read(bufferSize);
int size = ByteBuffer.wrap(buffeSize).asIntBuffer().get();
byte[] buffer = new byte[size];
inputStream.read(buffer);

// convertimos el InputStream a byte[] para pasarlo a ImageIcon
byte[] binaryImage = new ByteArrayInputStream(buffer).toByteArray();
return new ImageIcon(binaryImage);