First of all most if not all bad reactions to wine are not allergic. A true allergic reaction involves an immune response to an allergen, usually a protien, these are very rare, more common are food intolerance, where someone has a reaction without the immune system being involved. Lactose intolerance is a well known example.
As far as likelyhood of a food allergy occuring vs some other trigger, in double blind placebo studies around 2% of the population have true food allergies. This compares to roughly 20% of people who self diagnose food allergies. This means if you think you have a food alergy, there is a roughly 1 in 10 chance you actually do.
Most medical allergy experts do not think adverse reactions to wine are true allergies. There was however a recent Italian study that identified two protiens in wine, endochitinase and a lipid transfer protien that did casue anaphylactic shock reactions. So there is some disagreement in the scientific community if wine allergies can be true allergies.
The most likely cause of the symptoms reported by this poster are ALDH deficiency. Acetaldehyde is a compound formed by the breakdown of alcohol in the liver by the enzyme alcohol dehydrogenase. It's a toxic compound, and the one that causes hangovers. Most of the time it is broken down by aldehyde dehydrogenase (ALDH) into acetic acid. But, about 85% of east Asians (Chinese, Japanese and Koren) have a ALDH deficiency. Symptoms of ALDH deficiency are flushing when alcohol is consumed, primarly of the face and neck. This deficiency is fairly rare in non Asian populations.
Dave_Tong, Steven and Alice both have ALDH deficiency, Steven's seems worse than Alice, that's why he rarely has more than 1-2 glasses at our parties. See if you notice it next time you come by. For a long time he thought it was a red wine allergy, and avoided red wines.
Sulfites are present in all wines, unless removed through filtration. They are not more common in new world wines. They are most common in German Reisling's actually. Sulfite reactions cause asthma like symptoms. They are very rare, and studies have been inconclusive thus far on linking them to asthma attacks in wine drinking patients.
If you suspect you are having a sulfite reaction, you should do the test Dave_Tong mentioned. Many foods have much more sulfite than wine. Two pieces of processed white bread (wonder) have more sulfites than a glass of wine. Dried nuts and prepared salads are also very high. It is highly unlikely you have reached the age to consume red wine and would not have already been aware of a sulfite sensativity from other foods.
Histamine is widely considered to by the true culprit in most people. Red wine contains 0.6 to 4 grams per litre of histamine, whites far less. It's thought that patients intolerant to wine can not degrade histamine properly due to a deficiency of the enzyme diamine oxidase. A recent study though showed no correlation between histamine content and red wine intolerance. If you suspect histamine's are the cause you may want to try an anti-histamine before drinking red wine.
The bottom line, is we don't know why people sometimes have bad reactions to wine. I'll quote Dr Ewan from Addenbrooke Hospital, Cambridge: "The sensitivity to wine is thought to be due to the direct effects of various - poorly defined - chemical components of the wine."
It is likely a combination of factors. The best thing anyone can do is consult a doctor. Short of that they should take detailed notes on the conditions they had prior to the reaction. Location, food, type of wine, clothing and any other factor that may contribute, and see if they can establish a pattern that is causing their intolerance.