What causes heel swelling (on the bottom part of the foot/ foot pad)?

Inflamation. Trauma, plantar fasciatis, hematoma are some causes.
Heel swell. Most common pathology is heel spur but callouses or warts or even an infection could be present., see a podiatrist.
Plantar fasciitis. Plantar fasciitis can cause pain and swelling of the heels. You will notice the pain especially when you take your first step in the morning. Try anti-inflammatories such as advil, motrin, Ibuprofen or naprosyn (naproxen) with food first.