Sounds like you have carrot flies... they burrow into your root veggies and are nearly impossible to get rid of once you have them... BUT you can avoid getting them by NOT thinning your plants. They are attracted to the smell of carrots and other root veggies and they will come calling when you thin them out. The best thing to do when you know you have carrot flies is to plant very deliberatly in rows with the veggies 6" apart. If you do not over crowd you do not have to thin.
Love Val