White gold is routinely alloyed down with nickel. Nickel causes allergic reactions in a lot of people.
It's probably showing up now, because your ring was plated in rhodium (the whitest member of the platinum family) when you bought it. This is normal, as white gold always has a little warmth to it, so it is almost always plated in rhodium.

The rhodium has worn off. The white gold, alloyed with nickel is in direct contact with your skin. You are reacting to the nickel. One easy solution is to bring the ring in to the jeweler where you purchased it and have it replated with rhodium. Or, you could trade the ring in for a white gold ring that does NOT contain nickel, a palladium ring or a platinum ring.
The metal rhodium is essentially inert to the skin, hypoallergenic, no reaction. What the reaction could be is a basic metals reaction and that SHOULD NOT be happening if the rings have a real rhodium plate.

My suggestion? Contact QVC and tell them of the problem. They should either give your money back or replace the item with one with a real rhodium plate!
Green is a reaction generally to base metals, such as copper, etc., which are either preplate(done beneath the rhodium on metals like silver) or part of the the meatal alloy the ring is made of.

Either the plate is not rhodium or is a poor job at plating. QVC owes you an answer on this one and your may use my answer when you contact them if you want.
Without seeing the ring and actually examining it, I can say little about the ring itself.

"Temporary Fix. Recommended for you to Try:
Rhodium is a hard and durable white metal. Most white gold is given a quick plated layer of rhodium when brand new or when repaired.

This thin layer of rhodium gives the metal a whiter look. Rhodium is also a metal that does not react with the skin. A local jeweler should easily be able to refinish, buff up nicely and rhodium plate your ring. The look is good. The advantage to you is the rhodium provided a safety layer between the nickel in the ring and your sensitive skin! The rhodium works very well when the plating is done correctly. You can expect the rhodium to wear off in time but you should get 6mos to a year of wear before the ring should be plated with rhodium again. We often do this service for ladies who love white gold earrings but have problems. With yellow gold problems, we plate the parts touching the skin and it works until the rhodium eventually wears away."

Is your ring white gold? If so, the rhodium plating by a local jeweler should ease the problem immensely and the surface will last a fair amount of time before redoing is needed. If the ring is yellow, there are likely environmental issues here, including swimming pool chemicals and salty air(if living near the ocean).

Chemicals will often build up in a microscopic way and lead to skin reactions or smudges. Salty air can lead to a build up of residue which will cause smudges or even some sensitive skin reactions. For yellow gold, the solution is difficult but involves either avoiding the environmental issues or cleaning the ring quite often(every couple of days) with a good gentle scrub with a gentle dish detergent and rinsing well.