If the infractions dont show on your drivers record as a DUI, you should be alright. Just make sure you are honest when you disclose the information.
I think your first move should be to obtain a copy of your driving record. See what it says and how it is worded. Every state formats their records differently.
There is a guy in my class with a DUI, he made sure that the airline was aware of this, and he still go the job