Ever see a photo of a polar bear in a blizzard? Well, if you've ever seen a mammogram of a woman who is lactating, that's basically what it looks like: white on white. Virtually solid white. In such a mammogram, there's no way to see anything that might reveal trouble inside.
When breasts are filled with milk, mammography is not a reliable diagnostic tool; we need to rely on a clinical breast exam and ultrasound. So, if you are due for your annual mammogram and are breast-feeding, wait until you stop breast-feeding—and then wait several more weeks—to ensure that the milk has dried up. Then go get your mammogram.
In the meantime, don't stop doing your monthly breast self exams. Though you may find it harder to differentiate lumps and bumps than it was before your milk arrived, it still is an important routine to continue.
And if you feel something odd, or if your baby is all of the sudden rejecting one of your breasts, see your doctor. Sometimes babies are quite smart in detecting when something is wrong, and they'll suddenly refuse to nurse from the side that perhaps tastes different to them.