false red light charge

What is the name of your state? IL.
I was pulled over for going through a "red" light. The police car was adjacent to me on the right (cross traffic) waiting for the light to change. I wasn't speeding and entered the intersection when the light was yellow. I explained that I felt I was past the point of no return to safely stop at the light and coasted through. He says it was red the whole time. Conditions were cold, dark and the ground was white with salt dust (almost like sand). I told him that I disagreed with his charge and that I would see him in court. He asked if I had any other tickets, I told him a speeding ticket from last summer for which I was on court supervision. He immediately said "hmm, ok- I'm going to give you a citation." How do I prove it to the court if it's me vs. the state, do I need an attorney. For me it's more a matter of principle than any insurance rate increases.

Why would you go through a yellow light when there is a cop car next to you? Also talking back to a cop is a no-no (even if you dont agree with the ticket, dont argue). I belive your gonna lose in court. Getting an attorney is gonna cost you a pretty and while it might drop the ticket, is it really worth the hassle?

Sorry that my post didn't explain that the cop was 90 degrees to my right (in cross traffic- adjacent to my car, not next to me). Also, I was very polite and I explained that I could not have safely stopped in time(did not argue or plead with him). When he disagreed, I was trying to indicate that he was incorrect (ie. not admitting guilt, since any statements are admissable), but in a polite way. Do these traffic attorneys that I here about take care of situations like this? Do I have a chance otherwise? Helpful info is appreciated.