This is very complicated, and I'm hoping that you'll stick through all of the steps with me. ;)
- Go to the store.
- Get bigger anchors.
- Return home and install bigger anchors.
(No, really, that's the answer. You can't patch the drywall and put anchors in; the most you could hope for would be re-drilling holes near to your anchor, but you really risk cracking the drywall if you do that. I'd just get bigger anchors.)
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:
![enter image description here](https://i.stack.imgur.com/HI2nX.jpg)
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
![enter image description here](https://i.stack.imgur.com/d4bAA.jpg)
Best Answer
Cut away any burs or rough edges around the unwanted hole. clean out any dust or loose particles.
fill with filler to a level below the surface of the wall (ie. indented) allow the filler to set hard.
Fill again below the surface of the wall, allow the filler to set hard.
fill again level with the surface allow the filler to set hard.
fill again slightly proud, allow to set hard, sand until flat.
paint to match, 3 coats.