If you are asking if the actual driving record will follow you onto your new state's driving record attached to your new driver's license then it would depend upon your new states' laws. Some states place your violations from your previous state's motor vehicle record (MVR) on your new driving record while others will not.
To find out if the new state will put your previous state's driving record on your new MVR ask their Department of Motor Vehicles (DMV).
Even if your driving record doesn't go onto your new MVR directly your driving record will still follow you. Insurance companies and employers will see that your driver's license was recently obtained in your new state so will check your previous state's driving record.
Also in many states when your license in checked by an officer in your new (current) state it will show you surrendered an out of state license. An officer may then be able if he has reason to request and receive information regarding your prior driving history in your previous state.
If your license in one state is suspended, revoked or cancelled than this information would be put in the National Driver Register (NDR) which is checked when you apply for or renew a driver's license and thus any state you go to would see if you have a problem with your license in your previous state.
You can get a car insurance quote here. Your driving record will be verified at the time you buy your policy and you will know if those violations have followed you.