In your lifetime, 3 is not too many. It is unlikely. Two in two weeks, no.
However, this is a genuine concern. Talk to the doctor ordering these tests. He should talk to you about when to be concerned and what would happen.
I wouldn't suggest googling this though. You'll get too many horror stories or people who don't know enough spewing opinions. Although a doctor may be biased (not all are, in this area at least) they are better able to evaluate the risks, especially in the context of the potential gain having these pictures will bring.
If it make you feel better, ask if they could let you use a shield on areas on your body that are not being pictured. They do have shields (think pregnant women) and most reputable workers would rather just indulge you to get you through than argue - though many will support your proactive attitude about your health! However, accept it if they say the area they need encompasses most of your vital organs so the shield won't fit in a beneficial way.
