Wawa:
You talk about an amp with a gain of 10, followed by a buffer (no schematic diagram).
But in your other post, I see a diagram with a gain of 69.
?
Maybe better to continue this in your original post.
There is only one A/D for all analogue inputs.
A MUX (multiplexer) is used to switch between analogue inputs.
A "ghost charge" could still be present from a previous read.
The output impedance from the driving circuit has to be low enough to clear that quickly.
The output of an opamp should be low enough.
Taking two consecutive readings, and only using the second one, is another way to tackle the problem.
Reading can also be influenced by Arduino's 5volt rail if you are using default Aref.
Did you check the output of the circuit with a scope.
Leo..