The points stand for a conviction, which stays on your record forever. However, the impact of the points only comes into play if you exceed the limit for points in a calendar year, which would result in a suspension.
Clarification: According to DMV the points stay on the record for at least 10 years, which allows for them to stay on indefinitely. Also the point accumulation regarding suspensions starts at 12 months and goes up to 36 months. Check the Florida DMV website, it spells out all of the specifics.
Counsel above adresses the point as part of the driving record. You must also factor in the cost of automobile insurance. If you just paid the ticket you agreed to accept the four points! ouch! In regard to the insurance companies..they used to request a three year copy of your record. They tell me now they can go back five years! Whoever told you to plea to a careless driving rather than fight it in court , provided you with poor advice..and I am sure it was not an attorney. Be aware it is one of the worst infractions to roll over on. I realize you may not have had the money for an attorney but remember, you can take a ticket to court by yourself..the hearing officer would likely withhold the points if your DL record was not that bad.
Hope this helps..remember, everyone is a lawyer when you need advice..but they are wrong.