Problem of noisy ground
Do you have a de-coupling capacitor on the motor itself? If not, add a 100 nF ceramic capacitor across the motor terminals, as closely as possible to the actual motor housing. (Worst case, across the connectors to the motor terminals on your board.)

Does the motor run only one way? If so, also add a dissipation diode across the motor, with anode towards ground.

To get a better measurement of the voltage across the sensor, you may be able to use Kelvin-style wiring (or "remote voltage sense" wiring) where the actual sensor wires are separate from the current carrying wires. Whether this works depends on how the ground for your 1.5V reference is created.

A separate battery for the motor only seems like a good idea. If you can't do that, at least put a voltage regulator between the 3.7V battery and the rest of the circuitry, regulating down to 3.3V or so. (You'll need an ultra-low-drop-out regulator, such as a LF33AB or better, to do this.) Regulators typically damp 80 dB or more of noise. Especially if you keep the grounds separate.