When you sow carrots, if the ground is dry water the drill thoroughly before you sow, then draw dry soil over the seed. That way the seeds are in moist soil but it doesn't evaporate as the surface is dry.
If you use a polythene cover over your carrots then obviously you have to water them.
A fleece or 'enviromesh' cover is better but it needs to be well held down along the edges and at the ends.
An alternative way to keep out the egg-laying flies is to build a barrier at least 18 inches high around your carrot plot - the easiest way to do this is to make a wooden frame and attach fleece to it. The female flies can apparently not fly higher than 18" - I have not found this method successful.
If you could grow them higher than that, perhaps on a wall or a shed roof in a fish box or bakers tray, that might work.
There are certain seed varieties which are resistant to carrot root fly.
I grow my carrots inside my polytunnel and still use a mesh mini tunnel over them - great carrots
Carrots can be slow to germinate, so a useful trick is to sow a radish seed every 6" along the row, as you do with parsnips, which are even slower - the radishes will germinate first and mark the row, so you can hand weed before the carrots germinate and pull out the radishes too.
Again, because they are slow to germinate, weeds can often swamp them before they emerge. One way to overcome this is to flame weed the whole area just before the carrots emerge. To know when they will emerge, place a small piece of glass over part of the row - this will bring on a few seeds early so when they come up, flame weed the rest of the row. The carrots will emerge a couple of days later into a clean and weedfree seed bed.
Probably the best approach is to do everything, including growing onions or other smelly crops near the carrots in an attempt to confuse the flies. Home grown carrots are so tasty that it is worth the hassle, but I do know just how disappointing it is to find all those lovely roots are infested with root fly maggots