I'm stuck on School district code even tho I didn't live in Ohio full time. I was only a student with a job.

 I take "I was only a student with a job" to mean that you are an Indiana resident attending school in Ohio. 

You should not be dealing with an Ohio School District income tax or even Ohio state income tax. 

In the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file an OH return.

Ohio has a reciprocal agreement, on wages, with all neighboring states. No Ohio state taxes are withheld or due and you do not need to file an OH return. But your home state will tax you on your Ohio income.

If Ohio taxes are mistakenly withheld, you have to file an Ohio return to get a refund. You should ask your employer to stop withholding so you don't have to file an Ohio return every year.

However the reciprocity agreement does not apply to local city taxes. You are not required to file a local city return, but you are also not entitled to a refund of the city withholding (box19 on your W-2), unless there was an error in the amount.  Most  IN counties (but not the state)  allow a credit, or partial credit for tax paid to an OH city. That will come up in the IN state interview. 

If you are filing an OH state return to get a refund and it's insisting on a School District code, enter 9999.