Same thing happened to me. I had to take an entire day off work and make two trips to the Social Security office (where I and the black ladies who work there were the only people who spoke English, and where they offered free translation services in 54 languages), and go back to Virginia MVD three times to get a new drivers’ license when I moved from the District. It was a nightmare, and I was born in this country. The Social Security office really freaked me out. It was full to the rafters of foreigners signing up for Social Security benefits that I have been paying for for years.
I lucked out, there was no one in the SS office other than me and the lady behind the counter when I went. And like you I was born here, as were my parents and grandparents.
MVD even gave my husband a hard time because he is a “Jr.” he had to provide his birth certificate to prove it was legitimate. Fortunately we had a certified copy of it and he was able to produce it quickly, otherwise we would have had to wait to get one from Massachusetts where he was born.
Getting a VA DL was a major hassle for me, and so I don’t see how illegals could eaisly acquire one, although I imagine in the more populous environs of NoVA controls aren’t quite as tight in rural areas like the Eastern Shore, just because of the shear volume of people.