There is no reason you "can't" have a mammogram while you're breastfeeding. Your breast tissue is denser while you're breastfeeding, so it can make it more difficult to evaluate the images. However, if there is something you and your doctor are concerned about in your breast, it's wiser not to delay working it up. Going to a center that offers digital mammography allows them to manipulate the image after it's taken to make it more or less dense and makes reading it more accurate - this would be ideal for your situation. If you're going to have one, I'd have it done digitally.
Also, some people tell you that you should pump and discard the milk after getting a mammogram. There's really no reason for this, as the radiation doesn't stay in your body or in the milk after the x-ray is taken. It simply passes through to give the picture.
I had to have a mammogram while I was feeding my last baby. Hope everything works out well for you!