How/When to file for motion to dismiss?

I was pulled over in Greenville, SC and told I was pulled over for speeding and immediately given an exit order and promptly arrested for simple possession of marijuana. After I was placed under arrest the officer began to search my vehicle very thoroughly and found nothing else. I was taken to Greenville County and was only given a citation for simple possession. Do I have grounds to dismiss based on the fact I was never issued a speeding citation therefore the stop was unwarranted?