Will swapping the input terminals on my op amp give me a negative reference voltage?
No, it's not as simple as swapping the input terminals.


You must still provide negative feedback for the circuit to be stable. By swapping the input terminals you'd have positive feedback instead of negative.
You need to provide a negative power supply if you want to get a negative output.


You can google "op-amp inverting amplifier" to find examples of the circuit you want.

The standard inverting amplifier does not have "near infinite" input impedance like the non-inverting amplifier does, so you'll also want to account for the amplifier circuit's input impedance loading the voltage divider if you need a very particular output voltage.