Hi Lisa Jean & welcome!
I am not a carrot expert by ay stretch of the imagination, so I could be completely off here, but my first thought is it's way too soon to start worrying! First, be sure that you've thinned them according to the
seed packet instructions. I think for this variety it's one
seedling for every one inch, but check the packet. (If you didn't thin, and the tops are more than a couple of inches tall, use scissors to snip rather than trying to pull.)
This variety of carrot takes about 70 days to mature. Carrots-- the parts we eat-- are roots that are specialized as "storage" structures. After only one month, there's nothing much yet to be "stored"! If the tops are looking good, then I'd say that's good! They are photosynthesizing their little hearts out right now making lots of sugar that's being used to make more tops to do more photosynthesis. The plants won't start "storing" this energy in the roots (as sugar & starch which is why carrots are so delicious) until the season starts changing-- which is the signal to start developing the "carrot".
P.s. My mom's in G'boro & has heavy clay and she grew carrots just fine.
Carrot experts-- does this sound right to you?