Yes they are using a very small amount of radiation for chest X-rays. But CT scans, especially of the brain and abdomen, have a much larger amount of radiation, and repeated tests are not recommended unless absolutely necessary.

The risk of an X-ray is the radiation exposure. People are exposed to radiation from different sources all of the time. It is known that at a certain level of exposure, bad things can happen. What is not known is the potential random effects of radiation, even at low levels. In theory the risk increases with a younger aged individual.
Modern X-ray equipment is designed to minimize radiation exposure, but radiation cannot be completely eliminated. The increased radiation from a single X-ray is negligible. However, any radiological study should be taken into consideration with the risk of not doing the study.