Current to Voltage Converter in CMOS
If, as you said, an uncompensated 2-stage amplifier is unstable then you have answered your own about whether or not you need compensation.

To check for stability, I would create a circuit simulation at the transistor level that includes all relevant parasitic capacitances and resistances. Then perform an ac simulation out to a few megahertz, looking for changes in gain. You might also want to run transient simulations while slowly sweeping the frequency. Be sure to do this for a range of dc bias conditions.