Civ 5 - told I lack iron but have an iron mine?

Do you literally have to have an iron mine for EVERY SINGLE unit which requires iron?

Basically, yes. That's how Civ 5 handles strategic resources.

In Civ 5, strategic resources work like a population cap: The amount of resources dictates how many of a unit you can have at any time. You'll get the resource back once the unit that needs it dies, or changes into a unit that doesn't need the resource.

If you need more resources but don't have any more in your territory, then you can get them from friendly/allied City States, or through trade. If you end up needing more of a strategic resource than you have access to (e.g. by losing territory, losing a City State, or when a trade ends), then any military unit that uses the resource will be subjected to a large combat penalty until you no longer need more of the resource than you have.

Note that if you receive troops from friendly/allied City States, those will also use up your resources.