Will I be charged with public intoxication if I didn't sign anything and I wasn't given any test to prove I was intoxicated?

I was arrested or detained but they never read my Miranda rights. They never told me why I was detained until I reached the sheriff jail station even when I asked the office if am being detained. If not, if I was free to go and he told me I was being detained but he never answered my question. He was pushing me to sign a document stating the I have been arrested for being drunk in public. I refused to sign the document and he took me to jail for that. They were also pushing me to sign the document over there at the station which I still refused to sign because I wasn't intoxicated and I was not going to incriminate myself on the charge that has been put against me. I told the officer and the coronel. After spending about 20 minutes, they finally took me back to the city from where they arrested me from at the local police station and finally told me if I had someone to come and pick me up. The officer that arrested me at first offered me if someone could come and pick me up before being detained and I said yes but he never gave me the change to call someone. He just took me in. Also, they never did any kind of alcohol test on me to prove that I was intoxicated, nothing not even at the sheriff jail station or from where they pick me up. At the sheriff station, they never run my finger prints or took a picture of me at the sheriff station. Now I wonder if I have any criminal record but they ask me for my SSN which I had any problem and provided it to them. A few minutes before they released me at the local police station and officer came to me and told me that a judge will contact me and the I was going to spend 30 days in jail for apparently for not signing this document. Should I need to worry about anything? Did they follow proper procedure when they detained me where cops have a bad habit of accusing people unfairly?