Your AM modulator has a 80kHz square-wave for its carrier. Then it produces interference at all the odd-harmonics:
240kHz, 400kHz and higher. The odd harmonics at 560kHz, 720kHz, 880kHz, 1040kHz, etc will cause interference on the AM Broadcast band.
I told you that the microphone needs to have a preamp circuit to increase its output level from 5mV it is now up to 150mV which is the level from the MP3 player. Then the gain of the preamp must be about 150/5= 30.