Hello I need to know if I will go to jail when I try to renew my registration for my car in tx

I got pulled over for supposivly running a red light which I did not and during the process he also gave me a ticket for a bad tire. I was in the left turn lane and was the fourth car back in line by the time I made it to the intersection to turn the light turned yellow then red I could not stop I would have got hit. I tried to call the court house to set up a trial by jury which is what the constable said to do and they told me I would get something in the mail with my new date. Well that never happened and now I have a warrent that I can't afford to pay. My main question is I need to renew my vehicle registration on my car and I need to know if when I try will I go to jail? If you can help would appreciate it a lot thank you