While folks are telling you to check the spoke tension of your wheels, you also need to understand that once wheels are tensioned into a working range, increasing the tension does not make a wheel stiffer. Stiffness is determined by the elastic constant of the materials (Young's modulus) and remains the same regardless of tension. The only to get a stiffer (less deflection per unit force) is to use stouter materials, either more or larger gauge spokes, or a heavier rim, or both.

Test for deflection by holding your seatstay and pushing the rim across at the brake shoes with your thumbs. You can also test the lean flex by leaning the bike over a bit and gently pushing frame at the rear dropout with your foot, while watching for flex at the brake shoes.

If, after aligning the wheel as well as possible and checking for hub play, it still flexes enough to touch the shoes while riding, and the brakes are already as open as you feel comfortable with, only a new stiffer wheel will help. Before you spend dough confirm that it'll make enough difference with a borrowed wheel.

One last, but maybe the best, option is to find a rear brake caliper with a lower leverage constant; one which opens/closes more for a given amount of cable pull than yours. That will give you extra shoe travel allowing greater clearance, but still function effectively, though it'll need more squeeze force for given stopping power, which is rarely an issue for rear brakes.