How to heat an e-cigaret coil
Heating coils integrate the energy dumped into them to make an overall average dissipation. The PWM happens fast enough that the variation of thermal output is insignificant. 

The power dumped into the coil is proportional to the square of the PWM duty cycle. So at 50% PWM, you get about 25% of the max power. No need really to sense this directly, you can compute it.

That said, the coil will vary its resistance depending on temperature (it will increase some). You could characterize this by measuring the average battery current over the PWM range, and map this curve into your PWM setting.

Here’s some info about driving a nichrome wire heater with PWM. http://www.brysonics.com/heating-a-nichrome-wire-with-math/

If you want to measure current, it’s possible to do so by measuring the IR drop across the FET when the switch is on. As long as you know the Rds(on) of the FET you can get a good reading. Use a low-side diff sense amp circuit to boost the voltage to a useable value.