You do not say why her leg is paralyzed. If it from a stroke, many people get nerve pain in their affected limbs. There are conditions called neuropathies that cause a burning pain in the foot, which also is caused by nerves. There are medications that help these types of pain, which include neurontin, lyrica, ultram, antidepressants, and opiod pain medications. She can ask her health care provider about trying them to see if they help her.

One thing that concerns me is that you mention about her leg being discolored. Do you think her circulation may be an issue? If this may be the case, she needs to be evaluated by her health care professional to see what may be done to help reduce her pain from that problem.