what medications, including the cancer medications, are you taking?
your symptoms are very concerning to me. you could be throwing tiny emboli (clots) to your foot. having cancer causes your blood to become thicker, which makes you more prone to having clots. this could also be gangrene, which is usually seen in diabetics, but not always. being the back of the heel is turning black as well, i am thinking this may be the micro-clots as i mentioned. i would seek immediate attention, as you want to restore the vascular supply to your foot as soon as possible.
I don't want to alarm you, but I would go directly to ER and contact your physician on the way. Better to be safe than sorry. Keep me posted.