I have tremendous pain in my ankle. The pain shoots up my leg. I took a bad step on the stairs a couple of weeks ago. Could I have damaged tendons or ligaments? Should I apply ice or heat?

Apply nothing until you see your doctor for a diagnosis.

My dad once stepped off a curb wrong and broke his foot. You need to see a doctor.

As was mentioned... you don't know what type of injury it is yet... so you can't know what to apply. See the doctor... if you have torn ligaments, tendons or broken bones medical intervention is NEEDED for any of them.