I don't live in your state, but I got one traffic ticket a few years ago (my first and, believe me, my last) for running a red light. I had gotten careless in my driving and thought I could "do what everybody else does." The traffic officer advised me to go to court because I would probably be offered a deal, which would mean a reduced fine and reduced points. And that's what happened. Sitting in court, however, was an eye-opener. That judge was perfectly fair, but anybody who came in with an attitude went out with an embarrassed face and a much emptier wallet!
You'll need to talk to your insurance agent about your rates. Even if the company raises them, there may be things you can do to lower them again.
All those pesky traffic rules are, indeed, a big deal. Inflicting damage on people and property, even when you didn't mean to, are serious crimes; that's why there are ticketable offenses to help *keep* such crimes from happening. And everybody, but EVERYBODY, is embarrassed at being caught.