Driving while license suspended in state of Florida?

2 months ago I received a ticket for lack of proof of insurance (i had ins. just no proof w/ me). I paid the ticket at the clerk of court, was told my license would not be suspended and I was good to go. Few wks go by and I get pulled over for a blown headlight and the cop informs me that my license is suspended and gives me a $148 ticket. I call clerk of court (where I paid my ticket) they said it was the DMV that suspended it. So I call the DMV and was told that my license was suspended for not showing them proof of insurance (don't remember anyone telling me to do this) so I asked why I wasn't notified, they say that the DMV suspends the license and then mails out a notice (this makes no sense to me as there would obviously be a period where my license would be suspended without my knowledge). I give the DMV my insurance policy # and my license is reinstated. Also, the license was suspend on June 27 and I received the ticket on June 30th. What can i do to contest this ticket or should I even try? I do not want points on my license for this and have also been told that this could prevent me from getting some jobs.