Yes, Alabama can tax your earnings from TN. If you're a full-year resident of Alabama, Alabama can tax ALL your income, regardless of where you earned it. If the state section of your W-2 is blank, that would indicate that your employer did not withhold any Alabama state taxes. (They would not have withheld TN taxes, because TN does not have an income tax on earnings from work.)
In the My Info section of TT, enter AL as your state of residence, and answer Yes to the questions about earning income in another state. Enter TN as the other state. This will result in TT entering your TN earnings on your AL return.
If you still work for the same employer, I suggest you check with their payroll department to see if they can start withholding Alabama state taxes for you. If they are unable to do that, you may want to start making quarterly estimated tax payments to Alabama.