really hate hearing my amp through headphones
How do you hear the amp through the headphones?
Is the mic picking it up?
If so face the mic away from the amp, or move them farther apart.
I record with headphones, as using monitors while recording is just asking for trouble.
Record with headphones, then listen back to it through the monitors after (with the mic off or turned down).
Knowing how things are routed when you have this issue would help us answer.