It has been below zero here in South Dakota just a couple of times this winter. At this time of the year, we see about 5-10 flies a day. They swarm around light bulbs or by the stove when I am cooking. We haven't used insecticide spray because I do not like spraying things in our house, we have three small children. Anyway IF that worked, it would only be temporary.

South Dakota is a long way from Texas so a local expert should know your insects better. I've given you the link to your state Extension Service office. They can help you with identification.

You did not mention any particular livestock operation or any other obvious source of the flies. Therefore, I would guess that the flies are cluster flies. These flies are parasites of earthworms. Adult flies enter homes primarily in the winter as a shelter for the winter. The two approaches that I suggest are exclusion and the use of insecticide you have already mentioned. The use of screens, weather stripping, and caulking will help keep them out for the long term. You may want to check the attic of the home because that is where many of them spend the winter. Also look for entry points around the eaves of the house or vents.

Insecticide use will alleviate the problem for a short time. Even aerosal treatments with one of the pyrethrin products should help. Insecticides used according to the product label are quite safe but I understand your concern about the safety. You may want to hire a pest control operator to assist with this problem.