Brick drilling in close distance to another hole

Technically you could use some device for precision grinding like Dremel with some diamond bit with an extender to make it long enough, but that's almost mission impossible to do. First, you risk damaging the existing cable. Second, doing such job in a hard material when the hole is long and narrow will take too much time and precision to be worth it.

You actually have two options. Option one is to drill another hole or maybe find some other way to lay the new cable. Option two is to disconnect the cable, remove it, drill a wider hole in place of the existing one, then install the old cable and the new one.

you definitely don't want to drill into the brick. Drilling into the mortar isn't too bad though, and easily repairable if ever desired.

I've used Tapcons for anchoring into mortar. They work well:

The box will say what size masonry drill bit you need to pre-drill, then you just screw them in with your driver like any screw. I'd suggest longer is better (though no longer than the width of the brick, as that may be as thick as the brick is.)

Also, make sure this brick you are drilling into isn't a chimney. If it is, make sure it's either not in use, or has a metal flu inside (and don't puncture the flu)

Your idea of installing a wood cross-member into the brick and then hang something from there isn't a bad idea. I'd suggest 3 screws, then perhaps attach peg board to that, hanging the pots from peg board ala Julia Child