There is something on the back of my heel that sticks out like a mound. It is very hard like bone. Cardio exercise bothers it. Solutions and options?

Achilles exostosis. Sounds from the location that you may have bone formation in the insertion of the achilles tendon. A specialist for the foot and ankle can better evaluate this for you and offer you treatment options.
Great Q 4 POD, ORTHO. I referred this question to experts in foot care from podiatry and orhtopedic surgery. Thanks for asking. From all of the answers provided, it appears that it might be time for a visit to a foot specialitst to confirm a diagnosis and prescribe therapy, exercise options and proper shoes.
Spur. You may have a bone spur on the back of your heel. It would be bothered by the shoe as your foot moves up & down in the shoe. Try to put a pad around the bump and see if this helps by removing pressure. You should probably have it x-rayed to see the exact cause.
Retro heel spur . It's called a retrocalcaneal heel spur. Initially treated by stretching the calf muscle getting fitted for orthotics and physical therapy. I would limit any activity with incline. If you still have pain then it can be surgical addressed. Recovery is about two months.
"Pump-bump" An enlargement on the back of the heel is commonly a combination of swelling from a mild achilles tendonitis, possibly in combination with a posterior spur, or and enlargement of the bone known as a "pump bump". It is a slow healing process that responds to a combination of heel lifts, stretching, ice, oral antiinflammatory meds and in our office, laser therapy. Other pt modlaities are also used.