Is there an aviation career where I would help design an entire aircraft and its systems?
You were born 100 years too late.
In order to be an improvement over existing designs, airplanes become ever more complex and every detail is optimised over years and years. The days when someone like Robert Hall or Kurt Tank would design and test fly their designs are long gone.
The best you can do is to design an experimental aircraft and maybe market it as a homebuilt or a kit plane. But forget about designing front-line fighters all by yourself: This by now involves thousands of engineers and the test pilots have very different careers from those of the lead engineers.