Carrot rust fly (Psila rosae) is a small insect whose larvae feed on the roots of carrots and related plants. The adult flies lay eggs in the soil near the plants, and the newly hatched larvae burrow into the roots.Their feeding creates the characteristic rusty-brown tunnels, usually concentrated near the outside of the carrot. Damage can allow secondary rots to enter, and heavily infested carrots may become bitter, misshapen or unusable. There can be more than one generation during the growing season.

How to Fix It
Once larvae are tunnelling inside the carrot, there isn't much you can do to save that root. 

Remove badly damaged carrots and don't leave infested roots in the garden.

The best control is to keep the adult flies from reaching the crop. Cover carrots with fine insect netting or floating row cover from planting onward, with the edges well sealed. 

Because carrot rust flies stay fairly close to the ground, sufficiently tall physical barriers can also reduce access. 

Rotate carrots and related crops to a different area and avoid planting a new crop beside ground that contained infested carrots.

Harvest promptly rather than leaving mature carrots in infested soil. 

Beneficial entomopathogenic nematodes may help suppress larvae in the soil, although results vary with species, soil moisture and temperature. 

For a home garden, exclusion with insect netting is the most dependable control.