First, do not worry. The discoloration of your skin is not harmful and won't affect the strength of your ring.
Discoloration caused by wearing your yellow or rose gold jewelry can happen for a few different reasons.
Reason 1) Metallic Abrasion
The most common reason for skin discoloring when wearing gold jewelry is metallic abrasion. Metallic abrasion is a result of makeup on skin or clothing. Cosmetics often contain compounds harder than jewelry, which wear or rub off very tiny particles. Finely divided metal always appears black rather than metallic, so it looks like jet-black dust. When this dust comes into contact with absorbent surfaces such as skin or clothing, it sticks, forming a black or green smudge.
To prevent this, remove rings and other jewelry while applying them, and clean skin areas in contact with jewelry with soap and water.
Reason 2) Corrosion
Another cause is the actual corrosion of the metals. Gold itself does not corrode, but its primary alloys of silver or copper will do so, forming very dark chemical compounds under moist or wet conditions. When you sweat, fats and fatty acids released can cause corrosion of gold, especially when exposed to warmth and air. This problem can worsen in seacoast and semitropical areas, where chlorides combine with perspiration to form a corrosive element that discolors skin. Smog fumes gradually attack jewelry and are evident as a tarnish that rubs off on the skin. Concave surfaces inside a shank form collection points that trap moisture and contaminants, also causing dermatitis.
To prevent this, keep the area dry and remove all rings before using soaps, cleaning compounds, or detergents, and clean your rings frequently. As well as solving the problem, you'll be amazed at how much better your rings look!