Allergens
Here only the most common and widely known allergens related to wine will be mentioned. There are far more things that can be taken into consideration if one is suffering allergic reactions from consuming wine. Everything in wine, from natural components like grapes, ethanol and yeast can like the many additives and processing aides cause allergic reactions. As for processing aides, there should in theory never be any traces of them left in the wine, but unfortunately there are no guarantees for that, so caution is still advised.
Albumin
Albumin is the active ingredient in egg whites, a still common fining agent used for high quality red wines. Being a fining agent, traces should not remain in the wine after processing. Furthermore, now most countries demand that producers warn if the wine has been finned using eggs, to be on the even safer side.
Side note: salmonella from chickens cannot exist in wine (the alcohol and acidity kill it) and should not be a worry for anyone.
Casein
Derived from milk and mainly used for white wines. Only used as a processing aid and traces should not remain in the wine. But do avoid if you are badly allergic to milk protein, do not worry if you are only lactose intolerant, it will not affect you.
Chitosan
Derived from crustaceans and used as a finning agent. Works as quite an aggressive treatment and not commonly used. Main benefit is that it can help to remove traces of Brettanomyces from wine. Finished wines should not contain any traces, but since shellfish allergies are among the most life threatening, strong caution is recommended.
Gelatine
Rarely an allergen, which is why it is so popular. Diminishing in popularity though with the growing demand for Vegan friendly wine.
Gluten
Rarely found in wine, more common in beer, but sometimes it can also be found in trace amounts in wine. If so, it comes from an old-fashioned wheat paste that was used to seal oak barrels. Very rare and will only contain minimal trace amounts. Generally nothing to worry about.
Histamine
Histamine is a natural ingredient of wine, particularly high in red wine, and it has the last few years been receiving a lot of blame for causing problems like low blood pressure, facial flushing, nasal congestion and much more. Despite common believes though, wine is very low in histamines compared to many other sources. Foodstuff, like mature cheese, fish, meat, and yeasts usually contain ten times as much histamines as wine. So, unless you react to them as well, and if you do, please see a doctor, otherwise you are not allergic or even sensitive to histamines.
Isinglass
Derived from the swim-bladder of sturgeon and other fish. Nowadays often made from fish waste from canneries. Mainly used for white wine and beer, as a processing aid. Traces should not remain in finished product, but to be on the safe side, avoid if you are allergic to fish.
Sulphites
Strictly controlled, and rare to be allergic to, unless the person in question is asthmatic. Does on the other hand receive a lot of unwarranted blame, and many people ignorantly believe themselves to be allergic to sulphites, since it is the only allergen that has to be mentioned on the wine label.
Read more under Sulphur Dioxide