White metal used for rings can be either white gold or platinum. White gold is rhodium plated after manufacture to give it a more intense white colour. This plating will wear off over time and will need to be replated with rhodium at your jewellers. On the other hand, platinum retains its colour. Platinum is also harder than gold.
My bet is you have a cheap fiancee, and the ring's copper that was plated with a white metal.
A diamond solitaire ring is the traditional choice for an engagement ring. There are other options available, with the best choice being the one that suits the bride-to-be.
You can get a white gold engagement ring at many online and high street retailers. The biggest misconception about white gold is that it is primarily made of yellow gold.
With precious metal, everything is repairable!
Yes, the wedding ring and the engagement ring should be the same metal. You can purchase a set to make the two pieces work together.
Engagement rings are traditionally diamond so this would be the best stone to have set in a white gold ring for this purpose. If you would like to be less traditional then you could use ruby, diamond or sapphire, either alone or alongside diamond.
A platinum ring will wear away the plating of a white gold ring if worn on the same finger because platinum is a stronger and more durable metal than white gold.
In short, no, you do not have to have a special ring for the engagement. However, most people buy an Engagement ring for this occasion. Engagement rings are usually made of yellow gold, white gold, or platinum and usually have at least one clear diamond. To see an example of a traditional engagement ring, please see the resources/links section below.
In a store
Probably 18 karat gold/nickel alloy. White gold is gold mixed with nickel and looks silver.
You may want to have that ring checked by a reputable jeweler. It sounds like you have a copper ring plated in white gold and the plating has worn off the underside and is oxidizing from the moisture on your finger. White gold is Regular gold mixed with a white metal like nickel to change its color.
The finishes that one may get for an art deco engagement ring are gold and platinum to name a few. Many people also like the ring to have an antique style finish applied to the metal.