Is there a blood test that checks for deficiencies in the entire spectrum of all vitamins and minerals? If so, what might I ask my family dr. For?

Many ways to test. There are tests, but it's complicated. SpectraCell Labs offer a comprehensive test but I don't think it's always reliable: One can check blood levels of vits like A, D, E, B12 & folate (folic acid) but levels of other B's & C vary from day to day. Tests like show funtional deficiencies. See comment:
No. You should ask your doctor to be a great listener and to provide a diagnosis. You should provide your symptoms and complaints so they can arrive at the right answer without a lot of detour. Vitamin and mineral deficiencies are fairly uncommon. It is likely that your symptoms are due to something far more common.