Gary, I think you built my FM transmitter circuit. Mine sounds extremely clear on any FM radio with no clipping even when the sounds are loud.
I simulated the mic preamp circuit with an input level that is 11 times a normal conversation level and the output shows no clipping.
1) Maybe the cheap Chinese mics are no good.
2) Maybe the mic is connected backwards, its metal case should connect to 0V.
3) Maybe the transistor is bad or a resistor has the wrong value.
4) Maybe the radio is cheap and is overloaded by the strong transmitted signal. My cheap clock radio becomes overloaded by my FM transmitter and causes reception all across the dial.
You said, "There are some harmonic frequencies, the batteries are 9V" but there are no harmonic frequencies and there should be only one 9V battery.