What happens will depend on if you were at-fault or not for the accident. If you were not at-fault the other party's insurance will cover the cars to the extent of the policy limits. If you were at-fault then you will typically be held accountable and liable for the damages you caused. If the other party had uninsured motorist it will likely pay for their damage and then come after you for reimbursement for the money they spent.

If find out what type of payment plan you enter into to pay for the damages you should talk to either the other motorist or their insurance company or both. Since the police were not called to the scene you may not receive any of the penalties that you would have if cited for driving with a suspended license and without insurance. Both of these are serious offenses in all states so wait to drive until your license is back in good standing and get auto insurance as soon as possible.