how to filter out noise while measuring voltage across H bridge?
Here is a high-side, differential, current monitor that can run from a single supply voltage as low as 2.5 volts: -



Max voltage supply is 3.6 volts so it's reasonably suited for a 3V system.

It has a gain of 25uA / mV and this means if you use a 10k resistor (as shown above) the voltage gain is 250 and the output is ground referenced. This means that if 0.6 volts is regarded as equating to 200mA drawn by the motor, the shunt resistor (Rsense) need only drop 2.4mV at 200mA i.e. it has a resistance of 12 milli ohms.

This is far better than using a 3 ohm resistor because your will extend battery life.

As usual ensure enough filtering is present to counteract spikes etc. upsetting the digitization process.