The bony prominence on either side of the ankle are called the inner and outer malleolus. That term is however too technical to be used in the story I'm writing. Does the English language have any other terms for them?
Even though the malleoli are actually the lower ends of the bones of the leg, I think most people would simply call the bone the ankle-bone, if they had to refer to it specifically; even more common would be to use just ankle.
[ODO lists ankle-bone as meaning the talus. It's a complex joint and any of its bones or knobbles could be referred to colloquially as "ankle-bone".]
Outer ankle knuckle
could be a layman's term for the lateral malleolus