What could cause severe pain on the right side of my left heel?

Tarsal tunnel: Syndrome or entrapment of medial calcaneal nerve, posterior tibial tendonitits, plantar fascitis ?..It would depend on precisely where you are speaking of.

Heel pain: Could be caused by plantar fasciitis, this can be treated by otc arch supports and athletic shoes. If pain does not improve you should see your local podiatrist.

Plantar fasciatis: I suggest you see a podiatrist. This is a common problem and I am sure the dr. Can relieve your symptoms.