Deb,
In my training, there was a chart on how much radiation a bag was exposed to going through the x-ray machine. The highest level of radiation a person will get is from dental x-rays, the next highest was a passenger flying a typical 4 hour flight, the next was every day radiation exposure. The second LOWEST was the amount your bags get through the x-ray machine. The amount is so small that it will NOT affect your film or camera at all, no matter what anyone tells you. As long as your film speed is less than 1600, which almost everyone has, you will be fine.
However, at any time, you are allowed to request a manual search of your bag. I can't promise that the screener will be HAPPY about this, as it all depends on that person's attitude, but it is allowed. Just ask the screener that is handling the bags going into the x-ray unit. Or you can also just put your lead bag through and they will automatically search it as they will not be able to see what is inside your bag anyway.
You will be told that the x-ray will not harm your film, but if you are not satisfied, be firm and tell them you request a hand search of that bag.
This applies to CARRY-ON luggage. Some U.S. Airports have very strong x-ray machines used for CHECKED BAGS. You should always carry your unprocessed film with you in your CARRY-ON bags.
Your film that came out foggy, was it in your checked baggage?