I have flown during both my previous pregnancies and had no problems at all- I think the horror stories come during the third tri when women go into labor due to the pressure changes As for radiation, you can elect to have a pat down instead of a metal detector.
There is low levels of radiation in the atmosphere and we are constantly exposed to it. Flying is not going to significantly increase your risk. Pregnant women fly all of the time. I have flown multiple times this pregnancy and flew multiple times in my last pregnancy. Skip the body scan machines and try to relax.