Seriously, if the OP doesn't wan to over complicate things, just buy one of these IC's:
https://www.ti.com/product/CDCE913Tie a 10.7Mhz FM radio IF filter to the crystal inputs (may need to add a tuneable inductor) and feed his modulation to the Vctr input pin. TV audio 4.5mhz filters will also allow a narrower band. Also try SAW filters in the 10 to 30 mhz range.
You cannot use a crystal as they cannot be pulled far enough for FM radio's 200khz width.
Use the TI clock software to program it as it is I2C control.
TX from 10mhz up to 230mHz.
You will need to bandpass filter the output into a sine wave unless you don't care.
I still say make a proper 10.7mhz modulator and use a freq synth with mixer to transmit properly.