Can I get a pilot's license if my driver's license has been suspended?
The FAA has a guide on applying for a medical/student license  

https://medxpress.faa.gov/MedXpress/Content/Docs/MedXPressUsersGuide.pdf

Near the end, pages 30-33. They ask for consent to review your National Driver Register.  Read those pages, see if any of it applies to you.