Sorry, the images don't show anything that looks like an insect and I am not aware of any white flying insects that bite and burrow into skin. 

I would suggest you catch the potential insects if possible, put them in a small container or vial like a pill bottle and take or send them to your county OSU Extension office for identification. 

If you are experiencing skin irritation I would also suggest you visit your family doctor (and a vet for the dog) to receive a medical diagnosis and treatment.

Here are closer pics and I have captured an entire dog bed full so I have plenty of evidence and will be seeing the vet soon and give you and update

Thanks. It will be interesting to find out what they discover.