By "wing nut on the opposite side of the quick release", I presume you mean the right side of the bike, with the quick release being on the left side of the bike. The wing nut should not spin freely when the quick release is closed. Open the quick release, and tighten the wing nut a turn, then close the quick release. If it is still loose, repeat. Stop when the QR is difficult, but not impossible, to close. Keep in mind that you'll have to open it if you have a flat - so too tight isn't good, either. If nothing you do tightens the nut - take it to the shop.

Make sure your wheel spins freely, too, when the QR is closed, and doesn't rub against your pads. If it does, loosen the QR, readjust the wheel and then close the QR. You may need to widen the gap on your pads by turning the barrel adjuster a bit, too.

IF the QR is too loose, the wheel may flex under a load and rub against the brake pads.

The other scenario, which is what happened to me, is your rear wheel needs attention. The spokes may becoming loose and need tightened. Or, the wheel is possibly not rigid enough for your size and power.