FC, once you have a mosquito bloom, it's a tough problem to get a handle on without using a pesticide. I'm originally from Louisiana, and the mosquito is our state bird! Unfortunately, fogging/spaying becomes necessary unless you're fine with you and your livestock living with the mosquitoes and risking disease-borne illnesses.
When I have a dipteran outbreak (fly or mosquito), I use Tempo WP by Bayer. I don't raise bees, so that's not an issue for us, but Tempo will kill bees and other beneficial insects as well, so it's not a perfect product. What I do like is that it is a quick knockdown, and it degrades quickly as well. Sunlight degrades cyfluthrin, the active ingredient. The product has a half-life of 48-72 hours. Again, it's not a perfect solution, but IMHO it beats having to live with swarms of flies or mosquitoes.
A better solution for the future is to use agricultural lime (NOT hydrated lime). It's harmless to livestock; plants love it; and, it increases the pH of the soil over time so that dipterans cannot breed in the soil and puddles. It's cheap, and you can get it at
TSC or just about any feed store.
Also, I appreciate you editing your post where you responded to KG. She was just trying to be helpful. Be nice.