If you were assaulted and had your property damaged, the lowest possible charges would be a first-degree and second-degree misdemeanors. The statute of limitations for both is two years under Ohio law. Having said that, the longer you wait to file a police report, the more questions it will raise and it may harm the prosecution.
File a police report as soon as possible and if you have any physical evidence (photographs, physical evidence), make extra copies to provide to the police/prosecutor.
You have plenty of time left on the statute of limitations, which is two years for a misdemeanor. I don't think you really mean the legal statute of limitations however, but whether, as a practical matter, the prosecutor's office will file a criminal complaint over an incident that happened a month ago. If they are reluctant to do so, it's not because they won't do their job. It's because of lack of corroborating evidence.
At a minimum, you will need to file a police report. Most prosecutor's offices require this. If the prosecutor decides to then file a complaint, they will also seek a TPO (temporary protection order) at the arraignment if you feel this is necessary.
If after filing a report, the prosecutor is unwilling to file charges, they will inform you how you can file a complaint on your own, or you can seek assistance from the court clerk's office.
While I agree with the others that you have two years, do it now. Waiting gains you nothing. First, the problems may continue and second, too much time goes by and the prosecutor will be less interested. I hope you at least got the report made out eventually. Another good option would be a Civil Protection Order. See if there is a victim advocate office for help or you can file it on your own. In a very real way, it's more effective than a criminal domestic charge.