No you should be ok. I had 2 tickets but both were over 5 years ago so they were no longer on my record. It's a good idea to disclose them anyways. They seemed to appreciate my honesty even though I didn't have to. From what I've heard 3 tickets still on your record is the disqualifying number.

Just put the app in and relax. It sounds like you have the same issues that most of us do, and i assure you that you still have as good a chance as any.