My advice is to go online (if that is an option) and pay your fine. You may be more likely to be in the hands of immigration if you ignore your fine and later the court issues a warrant for your arrest for failure to appear in court. It's an unpredictable world, but I don't see people come into contact with immigration by paying speeding tickets. I hope this helps. And by the way, there's a pretty good chance immigration knows where you are already, but the odds of them "getting" you are statistically on your side, in my opinion.
If you received a speeding ticket, then presumably you received it from a police officer, correct? So it seems to me that if someone wanted to detain you, then they would have done it when you were already basically in custody.
You need to pay the fine.
And separate from the fine, you should probably consult an immigration lawyer to see if there is any way to 'regularize' your visa status.