It's hard to tell what initiated the stress (maybe irregular watering before you bought it, where it dried out more than it should have). Although we can't see the state of the roots, the rest of the plant looks fine otherwise, and even if the discolored leaves fall off eventually (which would be normal as a stress response), we think it will grow back well.

Larger containers are more insulated from heating-up and cooling-down as quickly as small pots (heat insulation is good for summer, and chill insulation is good for winter, even for cold-hardy species because they're more vulnerable to root damage over the winter when kept in pots). Larger pots also don't dry out as quickly, which is a useful feature for moisture-loving species like Swamp Milkweed.

After it settles-in from any transplant shock (give it about a week to adjust to stress from the move), you might want to lightly fertilize it to give it a nitrogen boost to encourage more new growth. Any general-purpose liquid or granular fertilizer should be fine; if possible, just choose one that focuses on nitrogen, the N in the N-P-K primary nutrient analysis on the label. Follow its directions for dosage amount based on pot size; don't over-apply, but applying a little less is fine to avoid stressing the plant's roots. Nitrogen is a nutrient that can help stimulate more leaf production as well as keep those leaves more green than yellowish or reddish. Fertilization is optional, though, and you may find that after some time in a new, larger pot, the plant produces better-looking new growth on its own anyway.

There is no specific potting mix to use (be sure to avoid garden soil, though, as that will be too heavy and prone to root-suffocating compaction compared to potting mix). Anything that retains enough moisture, or which you can water often enough to keep moist, will suffice. (No need to choose a product with added moisture-absorbing granules, though, which aren't proven to work well anyway.) The container should have at least one unobstructed drain hole in the bottom (or the ability to drain excess water buildup if it's a self-watering style pot). Fortunately, as its name implies, Swamp Milkweed is found in fairly wet soils in nature, so is more forgiving of accidental over-watering than most perennials.

Full sun is fine for this species, but if it helps with recovery and stress reduction in the short term, you might want to experiment with keeping it in partial shade for a week or two after transplanting. Leaves that have yellowed or become reddish like this usually won't turn green again, but any new growth should stay greener if the stress on the plant is easing.

Miri