From your description, it does sound like carrot rust fly damage, which is a common problem when growing carrots.

Carrot rust fly larvae attack the roots, causing young carrot plants to wilt and collapse. Once they are in the crop, they can be very difficult to control, so prevention is usually the best approach.

The best way to reduce carrot rust fly is to rotate your crops and avoid growing carrots in the same area each year. Ideally, do not plant carrots in the same spot for five to seven years. This helps break the pest cycle and reduces the chance of repeated attack.

With your current crop, you may need to accept that it is likely to be poor, as carrot rust fly is notoriously difficult to deal with once it has invaded the carrot patch.

When growing carrots again next season in a different area, they will do best in a light, well-worked soil cultivated to a fine tilth. Remove stones and lumps of clay before sowing, as these can also cause carrots to fork, split or become misshapen.