Jewelry changing color can happen because of different reasons. Chemicals, lotions, chlorine in water, all of these can change the color of some metals like white gold. If your skin is changing colors you may be having a reaction to one of the alloys in the metal your wearing. See if this reaction happens with all metals that you wear to try to pin point your allergic reaction.
Stop wearing costume jewelry.
http://www.helium.com/items/597008-why-do-some-jewelry-metals-turn-skin-green
If it is low carat gold (10 or so), the alloy metals might react to your skin. Anything but 24k will have some alloy in it, and jewelry is rarely made of 24k, since it is so soft. If you are highly sensitive to the alloys, even a small amount might cause a reaction. Furthermore, you sure your jewelry is really solid gold, and not plated? Plated jewelry will often react with the skin as you have described.
The reason some costume jewelry turns skin green is because the outer plating has worn off and the copper alloy metal underneath is exposed. It is the copper in the metal that is turning your finger green.
Silver jewelry turning purple can be caused by chemical reactions with sulfur compounds in the air or on the skin, tarnishing the silver. This tarnish can result in a purple or blue hue on the jewelry. Cleaning and storing the jewelry properly can help prevent this discoloration.
Skin reactions to jewelry are most commonly caused by a nickel allergy.
The only thing that is not a chemical reaction is the hot glue gun melting the glue. A copper bowl tarnishing, a spoiling peach, and jewelry turning your skin green are all chemical reactions.
It is best to by hypo-allergenic metal body jewelry for sensitive skin.
Sodium is a very reactive metal that tarnishes quickly when exposed to air or moisture, making it unsuitable for jewelry. It also reacts with many other chemicals and can be dangerous to handle due to its explosiveness in contact with water. Therefore, it is not a practical or safe choice for making jewelry.
Yes
I think it is bad for skin
Wear only high-purity, non-reactive precious metal jewelry made of gold or platinum, or at least make sure it's well plated with something durable and non-reactive if cost eliminates the former option.