Your PA drivers license is meaningless, unless you still maintain a residence in PA. Even then, it's unlikely that you are anything other than a part year resident of both PA & OH. You may have heard of a reciprocity agreement between PA & OH. That only applies to full year residents and is not applicable to city income tax.
Some Ohio Cities have an income tax. Any Ohio city, with an income tax, is allowed to have withholding taken out of your pay while you worked in that city. Your employer is required to do that withholding. You can't get a refund unless it was improperly withheld, i.e. you didn't actually work there for all or part of the time that your employer was withholding. If you live in a city with an income tax, you are subject to that city's tax as well. The city you live in will usually allow a credit or partial credit for the withheld tax you paid to the work location city.
You normally only have to file a return in the city you live in. It is not necessary to file one in the city you work in, if different.
You will file a part year Columbus city return. If your employer did not withhold New Albany tax, you should ask them what's up (e.g., your work location is not in the New Albany City Limits).
TurboTax can not, officially, do a Columbus City return. Columbus Income Tax web site https://www.columbus.gov/incometaxdivision/
