Yes, you should be able to find out how many points are currently on your Department of Motor Vehicles (DMV) record and what insurance points your insurer has listed for you.
DMV points are placed on your driving record by your state licensing agency after a court has notified them of your conviction of a traffic offense or after they are informed of you being in an accident or other situation that merits points in your state. To find out how many points are currently on your driving record you should be able to contact your state's Department of Motor Vehicles and obtain a copy of your driving record or abstract.
In many states, you can go to the DMV's website for instructions on how to get a copy of your driving history or MVR. The main ways given by most states is over the Internet, by mail or in person. A nominal fee of $3 to $10, depending upon your state's laws, is usually charge for getting a copy of your driver's history.
Your state's DMV should also be able to advise you how long a violation conviction and the points associated with it will stay on your driving record. In some states, the points come off your record after a few years while the conviction stays on for either a longer period of time or indefinitely (more typical for something like a DUI).
Insurance points are used to assess the eligibility for auto insurance coverage and for calculation of rates. These points are assigned by your individual insurance company, and each has their own type of "point" system. The system will vary, but many insurance carriers use the system based on the guidelines set up by the Insurance Services Office (ISO).
As for finding out your total amount of insurance points, you should contact your insurance agent and discuss with them your insurance provider's rating system and insurance point schedule. Your agent should be able to tell you how many insurance points you have accumulated according to the insurance carrier's records.
In many cases, the impact of older insurance points lessens over time. If your company adds insurance points for various traffic violations and accident claims, as time goes by and you receive no new violations and file no more claims, it will appear that you are a safer driver and these insurance points should be reduced. The reduction of insurance points is another issue to ask your insurance agent about when finding out your points total.
If you are currently paying too much for insurance, try shopping around. Comparison shopping with multiple car insurance carriers give you the chance to save hundreds, if not thousands, of dollars annually. (See "3 ways to save big on car insurance")