The standard heavy metal tests have a reputation for being deeply flawed. They are especially known for giving false negatives. I would also be skeptical of what your GP says since it's amazing how much ignorance there is about metals among health care professionals. That doesn't mean you couldn't give any reasonable suggestions he has a try, but I would keep a degree of skepticism and do some research first.
If I were you, I would probably find commonly described symptoms of metal toxicity (I guess aluminum is your main concern, right?) and see if you have many of them. Then investigate ways to chelate. Careful chelation shouldn't hurt you (assuming you don't have silver fillings now), so I would consider giving it a try and seeing it if helps. Keep in mind you would likely feel worse while you're chelating, and it may take months to see clear improvement.