What are possible causes of this weird heel pain?

Many possibilities: There are many possible causes from a heel spur to neuropathy (diabetic?). If you have tried rest, ice and nsaids and are still hurting after 2 weeks i suggest seeing a podiatrist or a foot and ankle orthopedic specialist.

Plantar fasciitis.: The most common cause of heel pain is plantar fasciitis: an inflammation of a thick band of tissue that helps hold up the arch of your foot. It attaches to your heel bone, and is usually the most painful for the first few steps in the morning, or after sitting a long time and then standing quickly. See your doctor to rule out tendinitis, fracture, or nerve entrapment.