Electronic – Trying to figure out what resistor I need

Your calculations are correct. I would give the resistor somewhat headroom, power-wise: if the LEDs' voltage is a bit less than 3.2 V, like 3.1 V (the voltage can vary by much more than that!) the current will rise to 22.5 mA, and the voltage drop across the resistor to 5.4 V. Then the power will be 120 mW, so the 100 mW won't do. Overmore, 1/4 W is a more standard value, and probably cheaper.

So go for a 240 Ω/0.25 W resistor.

I've used a 10 Ohm 5 Watt resistor in the past and it works well for testing both Zinc-Carbon and Alkaline cells - both "AA" and "AAA".

You will have a current up to 160 mA which is enough to load the cell and show its true voltage at that current level.

A new cell will have a voltage exceeding 1.5 Vdc (often above 1.6 Vdc); a used but still usable cell will have a voltage between 1.2 to 1.5 Vdc; a weak cell will have a voltage between 1.0 to 1.2 Vdc.

A cell with a loaded voltage less than 1.0 Vdc is considered to be dead. Some stuff might run from it but not for long.