EdS writes:

Can I get away with just painting over the concrete or do I need to
patch these areas?

Painting is not cost-effective because of a very short lifetime.

I did it myself, and also came up with a workable patching technique:

http://www.truetex.com/pool.htm

But from your description, it doesn't sound like patching would be cost-
effective, either; you need a complete replaster.

At about $1000/year in amortized maintenance alone, now you know why
residential pools are an extravagant luxury. Divide by the number of
annual swim sessions to get a cost per swim, and things start to look
exorbitant.