((((hugs)))) Sorry you are learning this lesson the hard way.

It's never easy to be wrong. The key is to learn from it, and hopefully it will save your life in the future (or others.)
Do you have the option of going to an educational class instead of getting points? The cost is the same as the ticket here in FL, I think, but you don't have court costs added.
Yes, it's ultra frustrating for other drivers to want you to speed and think tailgating is the solution.

I'm glad you got home safely though! TC