This is the logo for my new business, which by the way I start on Monday. (ITS HAPPENING!)

My problem is I want to use this image as a logo for T-Shirts and sign writing etc. But every time I upload it onto the 'make your own T-shirt" websites, the white backround stills appears. Is it possible to remove the white from the image and the blue lines to leave the black and red, with minimal fuss? Thanks in advance. :)