Talking here about type 1 IgE mediated wheat allergy. Not coeliac disease, which is an autoimmune process triggered by gluten.

Only 10% persists to adulthood, equivalent to milk/egg.  Max IgE over 20 has median resolution age of 7, rises to 16 if max over 50. Unusually, IgE often remains positive even when tolerance has developed! But trend still useful for individual patient.

Wheat allergens – most commonly LMW glutenin, alpha and gamma gliadins, NOT omega. Technically gluten is found only in wheat, and is a complex of gliadin and other proteins, similar prolamins in other cereals have different names eg zein (rye), avenin (oat), hordein (barley)! 

Level of omega 5 antibodies correlates with clinical severity of exercise induced anaphylaxis! Not specific though – Omega 5 antibodies are present in 80% with anaphylaxis to wheat (non-exercise induced) and 20-30% of wheat allergic with eczema. Useful for predicting anaphylaxis??

Note that those with grass pollen allergy often have non clinically significant IgE to wheat.

[Nutrients 2017 – doi: 10.3390/nu9010035]

Lots of different names for wheat versions/products – Bulgar wheat, couscous, durum wheat, freekeh, einkorn, emmer, farola, kamut, malted wheat, semolina, spelt, triticale, wheat bran, wheat germ.

Presence of wheat starch in gluten free products (can be useful for producer) means the low level permitted for coeliac disease may still cause reactions if sufficient amount eaten, so avoid wheat based gluten free products if type 1 allergy.

But glutens present in non-wheat grains are not usually a problem for type 1 wheat allergy, so excessively restrictive to follow gluten free labels on things not made with wheat, eg oats!

Testing often suggests cross reactivity between different cereals but when you actually challenge, majority only react to one, and non wheat allergies pretty rare. Oat, rye, barley, maize allergy uncommon.

And strange how aeroallergy (to the pollen) so rarely translates to food allergy and vice versa. 

[J ALLERGY CLIN IMMUNOL 1995;96:341-51]

So I would say no need to avoid or test unless symptomatic.

Cross contamination (as in coeliac) a big issue – crumbly! Toasters, butter, surfaces etc.

Hydrolysed vegetable protein sometimes comes from wheat, has to be declared as allergen but little evidence that it is still allergenic.

There are reports of allergy to deamidated wheat (“wheat protein isolate”), where tolerant to normal wheat. Found in cosmetics too.