I don't believe you need anything after U15, or possibly U10 as a low pass filter with the analog switch bypassed?
The sigma-delta ADC uses a switch capacitor input circuit that acts as a sample & hold.
Connect input high to the opamp out and input low to the mid-supply re (U22B). That circuit is configured to work with either polarity of current in the sense resistor, so "zero" is half supply, to give the widest range either way.
The ADC reference should be set to suit the maximum input range needed.
U22B input is presumably shown as 1.65V on the basis the circuit feeds an ADC operating on 3.3V
Use 2.5V (again, half supply; two equal resistors and a cap to analog ground) instead, if the ADC will run from 5V.
I'm guessing [hoping] you meant
"probably in the order of magnitude of 1.8 mΩ" - Milliohms, not Megaohms?
As shown, that circuit can only work as long as both ends of the sense resistor stay within the common mode range of the opamps; less than +/- 15V.
If you need a wider range, you need a different input circuit.