Pled "no Contest" To The Wrong Charge

Need Help esp. from Ohio

Hello. About 12 years ago, I pled "no contest" to an OVI in Ohio. I was obviously found guilty. I also had long standing plans to move out-of-state and the day I planned on leaving just happened to be three days after my sentencing. So, I made a decision, probably not the best decision of my life, but I chose to go ahead with the planned move and not complete the court's ruling.I knew that they would issue a warrant for my arrest and that I wouldn't be able to get my driver's liscense reinstated until I completed the requirements of the court. I also knew they wouldn't extradite me for an OVI warrant so basically I wouldn't be able to get my liscense. Who drives in NYC anyway, right? Fast forward 12 years, I'm now in California, in a somewhat better spot in life and wanted to put this behind me. The law states that I can complete the minimum requirements for an OVI in my home state, it's California now, and it would satisfy the requirements of the court as long as I also paid my fines ect... Well, I went on the courthouse website to check it out, it's been 12 years and I really didn't remember anything pertaining to it. When I logged in to the site, I noticed i was charged with an OVI-2nd Offense. It was my first OVI. I contacted the Ohio BMV and got my driving record which proves i have only been stopped once for an OVI. I then requested the sentencing footage of my trial. Upon my attorneys advise, you can see us conferencing before the judge enters the room, I changed my plea from "Not Guilty" to "No Contest". The judge then begins his spiel and says "OVI 2nd-Offense'. I must to have been paying attention or was too nervous to hear that part obviously. So, as it stands, I am guilty of an OVI 2nd-Offense, even though BMV records prove this was impossible for me to have committed. How do I go about fixing this? It's been too long for an appeal, but can't i do something because of incompetent advise of council? And it's really not about trying to get out of it, although if that's the case, I'll jump on it. I can't serve the penalty of the court because any documents I show to California will say "OVI 2nd-Offense" and I'll be forced to serve the more severe punishment. I've sought legal aid here in California, however, no one is willing to help me because they aren't liscensed in the state of Ohio. I will also most likely be doing this all pro-se as the fines ect.. only total around $1,200 and I'm poor and paying them would be cheaper than hiring representation. I'm fairly confident that, if I know the proper steps to take, I'll be able to research what to file and how to word the documents, and then have a legal aid society look over the documents to ensure I don't sound like a complete idiot. I just need to know the proper steps to take to get rid of this. Any advise would help. Thank you.