Unless you are after the distortion response of a specific amp, I would advise against miking your vocals twice as it will only increase feedback. You have two options here of which one was mentioned already by Mikko (try to avoid over-saturation and/or multiple distortion pedals in a row). The other option is to take note of monitor/pa speaker placement as the amplified signal coming through being picked up by the mic is responsible for the feedback loop (a certain frequency is picked up by the microphone -> gets amplified -> goes through speaker -> back to microphone ->...). If you want no feedback at all, ideally you would position the microphone in a way that monitored sounds are not at all picked up by its directivity area. If you want just a little feedback, you can direct the microphone more towards the speakers and experiment with that.
All of this also depends on the room you are playing in. I've had rooms where I was unable to use monitors cause feedback would interfer too much with my sound and other rooms where it was totally okay to experiment live with different feedback frequencies.
