Yes. If the police make a valid traffic stop for any reason, they can arrest you for DUI if they find "probable cause" to do so once they pull you over. However, speeding is not indicative of DUI, so there must be other grounds for your arrest. Perhaps your eyes were red, or your speech was slurred, which may have led the arresting officer to perform field sobriety tests (FSTs) on which you performed poorly.
But, even if your traffic stop and arrest were both legal, there still are several ways to challenge your DUI charges.