First, I am not a lawyer. But if you were not arrested and only "fine and cost," you probably did not even have a criminal background. Were you fingerprinted or booked? If not, I think you shouldn't worry.
I live in the South and all moving traffic violations are misdemeanors in nature and I got a "passing a stopped school bus" violation. I spoke with the BON and I even emailed a message to BON. I was told, "As long as you were not arrested, you don't need to report that traffic violation." My lawyer said the same thing. I also almost hired a lawyer who was used to work for Board of Nursing and he said the same thing. If you were arrested and booked, that will be a different story.
However, if a name based criminal search on a county level, you name might pop up. From what I know is that if you were not arrested, the "crime" will not be reported to FBI or DOJ. This is the reason why when you apply for a nursing license, you might ask to be fingerprinted because there is a fingerprint based criminal background check. But since you were not arrested, you should "relax."
The meaning of an "arrest" by definition is when a police officer moved you from one location to another for further processing such as mugshot and fingerprint. Just make sure you speak to a lawyer or ask for free on AVVO site, this web site has a lot of lawyers answering questions you might have.
This is America! There is always a hope somewhere waiting for you. You have to look for it. In Texas, if misdemeanor is 5 years old, the BON won't even do anything.