Sounds like nickel allergy.
That's the most common metal allergy (and it really is quite common). I have it myself.
Very VERY few people are actually allergic to pure silver or pure gold. Which are both as pure as pure platinum. But the laws allow you to alloy silver and gold (add other metals to them) a lot and still call them silver and gold, while you can only add 5% something else to 950 platinum, and what they add in that case is another member of the platinum group, not nickel. While sterling silver has 8% other metals in it, and 14k gold is only 58.5% actual gold. 18k is 75% gold, 22K is 91.5 % gold and 24K is 99.9% pure.
There's such a thing as 960 silver, which is 96% pure and also 980 silver which is 98% pure and neither are alloyed with nickel. But they don't sell them much in this country. Older Mexican and Central American jewelry are often this pure (and killer expensive here). Someone as allergic as you might seek this out, if you want to wear silver specifically. There are antique sites that sell it (and a lot of fakes are out there). Otherwise your best bet is probably to go with platinum, if you want a white metal.
You could also wear 22k gold, which I wear by choice. Even though the price of gold is way way up, 22k jewelry is still relatively affordable at Indian jewellers, because they don't have the markups that we have here. At a Chinese jeweller you can get 24k, which contrary to what you are told here, is NOT too soft to wear. It's too soft to set stones in, unless you bezel set, but makes beautiful and durable earrings, necklaces and bracelets.
There are some designers who work in this, Gurhan is probably the most famous one, but compare his prices (you can google him) to say, this website
www.goldpalace.com
I really think that the misinformation out there about the possibility of making jewelry out of purer silver and gold in this country is deliberate, as it allows jewelry to be sold that has such a small proportion of the actual metal in it, at high prices. Most other countries, even most of Europe(except England) consider 14k to be cheap costume jewelry, it's not gold there until its 18k (that is, at least 75%). Nickel is also banned for jewelry in most of Europe, so if you buy European made jewelry you may have better luck with your allergies.
Nickel allergy gets worse over time, is worse in your ears because you've had a hole put in there and the skin is sometimes open, and is getting to be an epidemic here with the trend towards body-piercing. It's no joke. Some people eventually get so bad that they can't even wear belts with buckles made of nickel.
Stainless steel is also hypoallergenic, so you're not actually doomed to a life of really, really expensive jewelry, if you have nickel allergy--but you don't have to mention that little detail to people (like husbands) who want to buy you stuff. (smile)