Hi,
sorry i wasn't near PC for a few days. Resistance of the coil is IMHO less than 4 ohms, because that would give you max. current about 2A. I think that you won't be able to measure the correct resistance just by basic resistance measurement on your multimeter. It's gonna be something like 0,1 - 0,3 ohms.
I would use 0,5A current source for a short time (if you have one, if you don't, use 5V voltage source and 10 ohm power resistor in series).
So connect your current source (or voltage source with that resistor) directly to the drill and measure voltage drop over it. Even better would be to use two MMs, one for current and one for voltage. Drill shouldn't be spinning and you should measure for less than few sec.
F.e. 0,5A over 0,2ohms will give you 100mV.
Btw. What is the method you are currently using for current shutdown? Did you use some dedicated chip?