I should probably clarify that both of the inputs are connected straight to ECG electrodes manufactured by AMBU and are professional quality.
Could you tell more about the input signal nature? How is the sensor output varying
Such a signal as the ECG requires a 1-10μF separating capacitor, otherwise you will see a strong drift.
The reason is the galvanic effect and the unstable resistance of the input circuits.
Install capacitors and wet the skin - this will greatly reduce drift.
In addition, the signal must have at least a small positive bias for correct operation of the amplifiers.
If project has some value other than having fun, I would recommend switching to PSoC5LP CY8KIT-059. PSoC5 has Del-Sig ADC which is superior for low-voltage measurements in noisy environment.
I second that ADC input must be differential with one or both inputs decoupled with capacitors (10uF electrolytes will do), and one of ADC inputs has to be connected to 1.2V reference (directly or through 100k - 1M resistor for biasing).