A question on current sensing through a very low resistor
How much current do you need to measure?

When using such a low resistance you need to be aware of the difference between simulation and realization. For a 1m ohm resistor you'd need kelvin connections to read appropriate values and make sure you have really low noise all around. 

Search texas instrument for low-side current measurement and you'll get off the shelf chips with the internal resistance.

This one is digital output:
http://www.ti.com/lit/ds/symlink/ina260.pdf

This one has analog output with gains from 200mv/a to 2V/A
http://www.ti.com/product/ina250

Search also maxim, analog, st, etc. There are a lot of products like this.

Cheers,