Is there any way I can run a license plate myself?

No.

This is to prevent things like identity theft,harassment,etc.

No. Can you imagine if we could? If you have a reason to believe this certain person who owns the vehicle is suspicious, you can go to a police station and file a report. They can run the license plate of the car.

It really depens on the two states (the one you are in and the one that holds the information) the ones that allow access for a fee usually want you in front of them at some point ,if the two states have a good recipricol agreement you might get lucky and get it locally but if they are a fussin and fuedin' you are on your own.When doing this for whatever reason have your ducks in a row and a real good reason-hope this helps

File a form at DMV it's called Freedom of the Information Act you'll pay $3 & within a week or 2 the DMV will send you all the info you need.I did this 2 my ex husband lol

you may be able to do it by contacting the local police department

I would say NO

no