You have carrot rust fly maggots. We used to have them until we started covering the carrots with a piece of row cover. We put it on in the spring when we plant and leave it on all summer. The carrots grow under it but the fly can't get in to lay her eggs.

Row cover is a light fine weave cloth that you can leave intact or cut pieces off. It's quite long so that's what we do. 85% of the light goes through it and so does the rain or water when you water. It raises the temperature under it by 2 degrees so it gets the carrots off to a better start in spring when the weather is cooler. You have to really anchor the edges though or it will blow off. Since we've started using the row cover we have had no damage from carrot rust fly larvae

Another critter to consider is the symphylan, which can be quite the pest of carrots and other root crops in some locations. I think of symphylans when someone uses the word 'pinhole ', for some reason.

It's pretty easy to see these little creatures scurrying around, though. A quick call to your local extension office might result in some good local information. If carrot maggots are common to your area, dowling has given you the best advice.

Let us know what you find out.