Here is topo using input analog multiplexer to calibrate the gain; ENOB Effective Number Of Bits is only 5.5, or approximately 50:1 accuracy, due to thermal noise floor.
7.8mV of the output KT noise is from that MUX; another 7.8mV from Rgain (100 ohms) in the DC-blocking series RC of non-inverting gain opamp topology (both stages use that topo, to avoid DC-offset buildup). And 6milliVolts from the first opamp (OPA211). The 2nd opamp is MCP655, a 50MHz opamp.
Here is the wide, tho DC_blocked, frequency response. Notice the resonance out at 10MHz, where the coil/sensor inductance peaks with capacitance of the analog multiplexer.
Regarding ERROR: neither opamp has satisfactory 1/GH accuracy at 100KHz, hence I suggested you consider calibration (one time). Another choice is 3 or 4 stages, with gain of 80db/3 (~ 21x) or 80dB/4 (10X).
To lower the noise floor, get rid of the analog multiplexor, reduce the stage#1 gain set resistors from 101_ohm and 10kOhm to 25_ohm and 2,500 ohm. Keep the OPA211 for its 1nanoVolt/rtHz noise density.
Finally, what is your interference environment? For 1% error of 200uVpp, the total injected trash (Efield, Hfield, VDD, GND) must be 2uV ReferredToInput.
Any black-brick battery charger within 10meters should be suspect.