Why would you stop something that is making you feel better?

According to the nutritional balancing cult you can have both high and low copper simultaneously. The claim is that you have bio-unavailable oxidized high copper and also low levels of useable copper. I have read this from other sources as well so I think it's a sound theory, but there is probably more to the story.

Zinc antagonizes copper.

If you are worried, just proceed very carefully. Imo copper probably does not need to be supplemented since you can readily get it from whole grains, nuts and legumes. If you eat meat/seafood then you can get it from liver or oysters.

If you are vegetarian it is hard to get appreciable amounts of zinc so that probably needs to be supplemented.

The same problem can apply to iron where you can have both high and low iron simultaneously... Schroedinger's iron.

Just go slowly and if you wind up supplementing either copper or iron take very low doses at first to test the waters.

Remember too that all minerals work in concert. Some of the basics agonists/antagonists are known. But no one knows the whole story yet.

People with copper problems usually have liver problems as well. Sometimes a series of Liver Flushes can unplug the the problem.

A good form of iron is ferrochel, patented from albion labs who license this to most of the major vitamin suppliers.

Chelating supposed oxidized iron with ip6 is a popular alternative cancer adjunctive therapy.

Beware of copper water pipes and copper cookware.

I doubt you will have problems if you supplement copper since usually when these types of practitioners prescribe Cu, it's always in relative to a higher amount of zinc... something like 1:8 Cu:Zn. But I've seen higher, like 1:10 or 1:17. Some people are hypersensitive to any form of copper supplementation though. Those cases are best with food sources, and even then it's best to be very careful as they might have to severely limit dietary copper.

And... we haven't even started talking about mercury, lead cadmium, or ionizing radioactive metals yet, the superoxidizers which could well be the smoking gun behind all of the copper craziness.

When in doubt just move slowly and carefully. Go at your own pace by regulating the amount of zinc you are taking. Too much zinc will pull more copper out than you can handle.

If you are daring you can look into the Schussler cell salt remedies. I have heard of people correcting anemia with them.