Thank you for the information and your question. Although you did have the duty to provide your DL information, you did not have to consent to having a photo taken of your DL. The other party, I would guess, is being overly cautious, perhaps because they have been tricked before by someone who had stolen someones identity. Hopefully, that is the case and not a case where someone will be using your identification information illegally.
Unfortunately, at this point, you can only react if something improper does come of this photo. In other words, you can file suit if your privacy is invaded by this person publishing this information on the internet, or you can file suit if suffer damages because they steal your identity. However, there really is nothing you can do at this point that will undo what has already been done. Photos these days are not in the form of film or a single copy that once it is destroyed or turned over it is gone. Also, since there was nothing illegal in their action and you consented, you cannot demand they give you their memory card, etc. So, that leaves the steps I mentioned if you are damaged in the future.
What I might recommend to make you feel more secure about your identity, is that you monitor your credit reports
for the next year with some regularity, perhaps once a month or once a quarter, to make sure no one has opened credit in your name that wasn't you. The other thing you can do is just put a freeze on your credit with the 3 agencies. That way they will not issue any new credit unless you specifically lift the freeze.
Please let me know if you need any clarification. I would be glad to assist you further if I can.