First Offense or Second Offense

My question involves criminal law for the state of: Ohio.
Almost two years ago, I got caught as shoplifting in NYC. I hired a lawyer and I got ACD (a diversion program in NYC), so my case was sealed and dismissed.
Recently, my parents got divorce, so I'm very stressful. I just have done a stupid thing. I got caught as shoplifting again:wallbang:. Police came, did smug shot, fingerprint and gave me a court ticket for a first class misdemeanor (the goods are under $1000). This case has just happened in Ohio. I thought my previous case was sealed and dismissed, so I told the police it is my first time arrest and first offense. He did not question me anything. So for the court hearing coming up, should I tell to my lawyer as well as the judge that this is my first offense?
My name in my previous case is a little bit different from my name in this case (last case did not have my middle name). My addresses are different too (One was in NYC, one is in Ohio). Also, two cases are happened in two different states, and my previous one was sealed and dismissed.
The court for this case is like a municipal court in a township in OH, so do you think they can access to my sealed case in New York City Court.
So this case is my first offense? or second one? I know it's very serious if they know this is my second one.
Could you please give me an answer? I'm very worried now, so please do not insult on me anymore. I know my very stupid, disgust mistake. I know I need a lawyer, but please let me clear about this first. I'm an international student. PLEASE HELP!!!

When you talk to the attorney you hire, you must tell him/her everything. They won't be able to help you if you don't. They can advise you on your answers to the court. Good luck.