Although the answer to your question depends on your state's official code, typically, most statutes state that you are guilty of leaving the scene of an accident IF you do not exchange information such as name, address, and insurance information. In this case, if you exchanged information as you have indicated, then you should be not be charged. However, again, it depends on the rules in your particular state.
there is a duty to report the accident if there was death, or injury, or damage to government property, damage to the extent of more than $200 "by quickest means possible." Sec 346.70. Fine is $40 to $200 plus costs. Unless you need an accident report for the insurance company, stop talking to the police.
Under sec. 356.70 of the Wisconsin Statutes, a person involved in an accident in which there is either resulting personal injuries or apparent property damage of $1,000 or more must "shall immediately by the quickest means of communication give notice of such accident to the police department, the sheriff's department or the traffic department of the county or municipality in which the accident occurred or to a state traffic patrol officer." Then, within 10 days of the accident, a written accident report must be completed. These are two separate obligations. If you are issued a citation for not giving "immediate" notification, you can attempt to contest the citation by arguing that it was not apparent to you at the time of the accident that the property damage was more than $1,000, and that, it was only as soon as you could make a reasonable inspection under daylight conditions that you were able to see that the extent of the damage to your car exceeded $1,000. There is a Wisonsin Attorney General's opinion that has interpreted the term "immediately" as meaning within a reasonable time under all of the circumstances of the case. It is not clear when you reported the accident, but if it was right away after you returned the next morning, and therefore within 8 hours of the accident occurring, you might be able to argue that this was within a reasonable time period under the circumstances. If you are issued a citation, you should consult with an attorney that handles traffic tickets to see if the citation can be dismissed. Good luck.