The case may have been initially rejected by the DA, but has been re-reviewed and criminal charges have been filed. A complaint is the charging document, so if you've been told a complaint has been filed, you're looking at charges.
What should you do? Get a lawyer ASAP. There may be things you can start doing BEFORE going to court to get you in the best possible position to avoid going into custody, having to post bail and possibly start toward reducing or dismissing the charges. You should also not discuss this with anyone except an attorney in a confidential setting. Assume anything you say to anyone will get back to the police and/or DA and will be used against you.
If you cannot afford an attorney, you can ask for the public defender when you go to court if you financially qualify.