First of all, every electronic circuit in this universe has, among others, a property called Electric susceptibility.
Second of all, your circuit has quite a high sensitivity giving that it reacts with your hand quite some distance away. It can also be said that your circuit is a highly sensitive antenna. Keep in mind that your signal is amplified by your amplifier, which looks like it amplifies even the smallest signals. If you build your circuit using a breadboard then it is highly susceptible to small signals.
I can recommend three things to do:
- use strong connections between components
- build a PCB
- reduce amplifier sensitivity
So I looked again at your circuit and I can see the POT with a 2MO resistance, having 1 pin left unconnected. You have 2 stages of differential amplifiers. In this case, varistor behavior is unpredictable which can be at maximum resistance thus gain is quite high. So besides strong connections, stable power supply, and so on, I'd also connect pin #3 on the POT to GND. You're actually modifying second-stage gain with that varistor.