ADC: μV measurement and noise
The ADS1148 is not the right ADC for this purpose. 

It has a differential input, which is useful if you want to measure positive and negative voltages. In your application the polarity is (most likely) fixed and therefore you are wasting half of the measurement range.

The differential input has a certain "input common range", which is the average of the two input voltages. It has to be within a certain range given by equation (3) in the datasheet. Therefore you can't measure small voltages or small currents in your case.

The amplification of the PGA should be such that you make use of the full range of the ADC. For example 2.048V / 10mV ~ 20. So 16 is a good choice. Without looking at the datasheet I would assume that the built-in PGA shouldn't degrade the performance too much.

The ENOB of 15 is OK and using averaging you should be able to get even more accuracy out of this ADC.