Those are certainly some kind of tick, with the three most likely kinds being the American Dog Tick (dermacentor variabilis), the Lone Star Tick (amblyomma americanum), or the Deer Tick (ixodes scapularis). These three ticks are native to your area. Additionally, all of these ticks has similar appearances when fully engorged as they are in your picture, making it harder to tell specifically which kind it is from the provided picture (and probably in general for most people). They absolutely could be falling off of your dog.
I strongly recommend you do the following:
- If your dogs are outside in wooded or grassy areas, you should avoid these areas to the best of your ability, or at least minimize the time spent in them. If you can, cut down tall/overgrow areas to reduce the chances for ticks to latch on your dogs (and yourself).
- You should probably bathe the dogs with a flea and tick shampoo. There are plenty out there on the market to choose from.
- Treat your dogs with some sort of flea and tick treatment, such as K9 Advantix (again, plenty of other options to choose from).
- Check yourself and your family members for ticks. Ticks are extremely small, with deer ticks being some of the smallest - especially in their larva stage. You'll want someone to give you a really good look over, especially through your hair.
It is possible to contract Lyme Disease from deer ticks, which could make this a more severe situation. I would check your dogs over for symptoms of this. One of the most common symptoms of Lyme Disease is a red bulls-eye like ring formed around the bite of where the tick was.
