TB skin test
Ok, TB skin test is a "requirement"... USCIS wants to see whether you had a +ve or a -ve reaction to skin test... Only if there is a +ve reaction, then you will need a chest X-ray. It may sound logical directly to do a chest x-ray, but it certainly appears that USCIS also wants to ensure that these procedural things are followed.
The medical exams are valid for only a year only if you do not submit the results to USCIS Once you submit ALL the results, they are valid until they make a decision, even if it takes 10 years. So, I would say, your doctor is not correct to repeat all the tests.
I assume that you have a copy of the initial form that you submitted. If so, if I were you, I would just ask the doctor to do a skin test and report the test result along with a copy of the old one. The choice is yours.