I had a negative mammogram but it caused a large, painful lump which isn't going away. Could it be cancer?

Hematoma? Sometimes a mammo can cause some local trauma and give you a hematoma (collection of blood) . Best to have it examined to be sure.
It would be. unusual, but possible for a mammogram to cause an internal hematoma that could feel like a lump. You should probably see your doctor to have it evaluated.
See your doctor. Any new lump in the breast should be evaluated by a physician due to the potential that it is a cancer, regardless of whether there is pain, regardless of a normal mammogram. While it is possible that this lump developed due to breast trauma, one would expect "black-and-blue" changes. More likely, compression from the mammogram could have made an existing lump more evident to you.