Your doctor sounds very judicious. Many of these “tests” have cropped up, but their usefulness has been questioned by our scientific board. Until they show you a direction besides watch and wait, they can be an expensive proposition (if not to you, the insurance industry). I think your plan is a good one, although blood work and chest x-rays usually don’t show much in regards to melanoma. What is important is: self exam (see our 2 minute video: http://melanomainternational.org/melanoma-facts/examine-your-skin
and know your skin to look for changes. Have your doctor examine your skin and palpate your lymph glands. It is better to have your doctor do that.
Then work on some mindful meditation to help your brain relax and not worry too much. We are always here to support you.