You can contact the prosecuting authority that handles the cases for the law enforcement agency that arrested you and they can tell you what the status of the case is, i.e., whether it is pending a charging decision or whether it has been filed or whether charges have been declined. But be advised that you may be alerting them they they need do do something with the case. The longer a case that is chargeable stays in a pile on someone's desk the better for you!
The quickest way on your own would be to contact the arresting agency. If you believe you should have been charged, you may wish to hire counsel to start checking with the arresting agency and the prosecutor's office. If you believe you have a warrant, again, you should have counsel begin the checks as any direct contact with law enforcement could result in your arrest.