You will probably never be charged. You don't need an attorney unless you either are charged (unlikely) or you want to file a lawsuit, in which case you should repost your question in the civil section. Your front yard is public, your backyard is not. Public means accessible to outsiders. The cops probably figured arresting you and letting you dry out in jail was an easy way to resolve their problem for the night. Sounds like an illegal arrest to me.
They did. Now whether it was justified or not is the reason you are going to contact at least attorney for a free consultation. Good luck.
The response above is not intended as legal advice since it’s impracticable to provide thorough, accurate advice based upon the query without additional details. It is highly recommended that one should seek advice from a criminal defense attorney licensed in your jurisdiction by setting up a confidential meeting. Moreover, this response does not constitute the creation of an attorney-client relationship since this message is not a confidential communication because it was posted on a public website, thereby publicly disclosing the information, which is another reason to setup a confidential meeting with an attorney.
In order to prove this charge against you, they must prove that you were "in public". That means actually out in public or in a place open to the public. Without revealing additional details online, you should meet and confer with a good local criminal defense attorney to discuss the facts and other defenses.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
Check the ordinance under which you were arrested it should appear on any citation you are issued. Usually for a public intoxication charge it has to rise to the level of disturbing others. It sounds like the police could not figure out anything else to arrest you for that so they just chose that one.