Water doesn't get "old" and rarely needs changing.

A much bigger problem of draining is ground water--it can turn your pool into a boat, even though it's concrete, and float it right out of the ground. Very, VERY expensive mess! If you don't have ground water, it's not a problem.

MUCH better than caulk is underwater epoxy, available at any pool store. Usually it's grey, and sets up nicely underwater. But it sounds like the pool needs resurfacing.

Others can offer more substantive advice.

Carl