Yes, as a matter of fact, unfortunately Ma'am, those are termites...not flying ants. Hopefully you never have to hear those words, however, as the weather warms up and the rains become more frequent, so do the activity levels of most pests....especially termites.
During the winter termites go deep under ground to stay warm and are virtually in a dormant state. As the temperature rises, they migrate toward the surface and eventually emerge from the ground.
Sometimes, unfortunately, they emerge in your house...from your wall...or your window...you get the picture.
This time of year is referred to as the termite "swarm" (or mating) season. The termite "swarmers" (also called alates) are the reproductive members of the termite colony, and they swarm out looking for a mate and a suitable location for a new colony.
This swarm may contain over a thousand swarmers which can be rather upsetting if you arrive home to find them all over your living room or kitchen floor. Although this is an unpleasant situation, take some comfort in knowing that the swarmers are NOT harmful to you or your family.
They don't bite, and in fact they actually don't even do any of the damage. However, the presence of swarmers does mean that there is a termite colony located somewhere in the near vicinity....potentially behind a wall or in a crawl space.
If this is the case, then it is time to consult a professional and get a thorough evaluation.