your post makes no sense. perhaps you missed something in there. did you have insurance on your car prior to 9/8? Why is your insurance company telling you that you were covered from some other insurance company when you yourself say that you had no insurance. and what does this have to do with the title. who owns the title makes no difference.
it sounds to me like you got in a crash, then went and purchased insurance. as for your new insurance holding a crash over your head that was not your fault, they will do nothing about it. they could care less, this all happened before you were insured with them. and if you think they will cover an accident that occurred before you purchased a policy with them, you are dreaming. there is no way they are going to have anything to do with that crash.
looking at your post, it sounds like you may be misleading your new insurance company. they can only base their answers on what you give them until they have time to look up the facts.
as for your ticket. i know very little about texas law, and can only offer an answer based on my experience in general. the ticket you received was probably for "no proof of insurance when requested". did you hand the officer an insurance card when he asked. if not, you are guilty. even if you had insurance, you are required to provide proof of insurance at the time of the crash. it is possible that the judge will drop it if you can show that you are now insured. it has nothing to do with you not being guilty, but his wanting to be a nice guy and give you a break.