LM386 and low-pass filter
Running your signal through a low pass filter is probably not what you want. Normally when feedback is an issue, you want to apply a notch filter with a reasonably high Q at the feedback frequency. That frequency is not trivial to predict and will vary with position of the microphone, the room it is in, humidity, and a slew of other factors. It's highly possible your feedback frequency will be around 2kHz or lower, and by the time you low pass the signal enough to stop the feedback, it will sound like your hand is on your mouth while you're talking. 

My first move would be adding an easily controllable gain stage ahead of the LM386, and take the extra gain away from the LM386. Turn it up until it squeals, and see if it's enough gain.