Why is my state income tax not included in the state taxes section? I am owing money to MI even though they took double what federal did.

The withholding payments sent to your state tax authority would be entered with your other income information in the federal part of the return. For a Form W-2, that would be Box 17. Please review your information there and other income forms and be sure they match your forms. Sometimes when they are imported, a field may need to be corrected. It is a good practice to review them and be sure they match the original. 
 

If you made a payment to your state that was not withholding, you will need to enter that into TurboTax. 

Go to Deductions and Credits
Scroll to Estimates and Other Taxes Paid and click on Show More

Select the type of payment made, for federal, state, or local