First, let me make it clear that this sounds like one of those times when you would be better off getting a pro to fix this - or at least troubleshoot it.
But having said that, I would proceed like this:
Disconnect the pump in question from the control system.
Test the output of the relay(s) -
Be sure it IS sending power to the pump,
Be sure it only outputs to ONE speed at a time.
Be sure it is not stuck 'on' for either speed.
Then test the pump -
Put power to the unit and see that both speeds work, one at a time.
Don't run the pump dry.
And go from there.
HTH