Did you let your phlox get acclimated in your garden before you planted it? Nursery plants are grown either in greenhouses or in warmer climates, and they are fertilized heavily to push lots of new tender growth, so they are delicate. You are right to be concerned.

You can create a mini greenhouse for you phlox with a bottomless milk jug (remember to remove the jug or just the cap during the day, depending on the weather) or cover it with a piece of cloth. Make sure there are no gaps around your cover (pile some soil around it).

Another concern -- your soil can still be too cold. When the sun is out, remove the mulch and let the soil warm up around the roots. As a rule, mulch your perennials in late spring.

Your Phlox is very hardy but since you just planted it covering it with a cardboard box would assure it not being set back. Open the flaps of the box and weight them down with rocks, bricks or whatever you have handy. Remove the box before the day warms up and replace again in the evening if another frosty night is in your forecast.