I understand how you feel. I have skin checks once a year by two different dermatologists. So basically I go every 6 months. This way, if one doc misses something, then the other might find it. I have had melanoma and I'm going on my 15 year anniversary since it was discovered. So I honestly welcome my appointments. I have had well over 35 biopsies and I am ok with that.
The most common form of melanoma is the superficial spreading type. It grows on the surface of the skin before it grows vertical. Therefore, it is initially slow growing for a lengthy period of time. Going once a year is often recommend for those of us who have had a melanoma because it gives the doc time to find something before it can turn into something nasty. If you are still worried about the doc missing something, then maybe consider doing what I do, and see another doc in between your yearly visit. And as always, check your skin on a regular basis.