Would it be better to cover my plants with a screen than to spray pesticides?

I have a few young plants and I noticed they have been hit by leaf miners. I under stand that leaf miners are larvae from from flies and other insects thar aren't too harmful to the plants, but have the potential to be. I don't want to spray pesticides on them so I considered hanging screen over them like the way screen hang over beds to prevent bugs. My plants are about three inches tall I was just wondering if that might be a better, easier, less harmful, maybe even cheaper way to prevent leaf miners.