The gemara‎{&&1}‎ talks about five grains that can be used for making matzot, two of which are in the wheat family and three in the barley family. The important point is not really their botanical name. Rather, it is necessary that they leaven in the way that wheat and barley do.‎{&&2}‎ However, we do not make assumptions about which grains are included in the list without precedent in classical sources. If there are grains to which you are not allergic, we will try to research whether they can be used for matza. Some are already being marketed (and, of course, should have proper rabbinical supervision).
Those who have trouble with matza due to its consistency may fulfill the mitzva by eating it broken into fine pieces‎{&&3}‎ or soaked in water if it has not dissolved.‎{&&4}‎ (This will probably not help for an allergy, but it can be useful for other issues). Furthermore, many of us tend to be particularly stringent on the amount of matza we eat on seder night. It may be that the absolute minimum shiur of a k’zayit,‎{&&5}‎ according to the letter of the law, will not affect you adversely.‎{&&6}‎
What happens if none of these ideas solves the problem? Certainly if there is even a faint possibility of a violent, dangerous reaction or of exacerbating a situation that could become dangerous over time, one should not take chances. However, if the reaction is less severe, the matter is more complex. The overwhelming majority of poskim agree that one does not need to make himself sick in order to perform a mitzva, even if it is not dangerous.‎{&&7}‎ Some derive this decision from the fact that one need not spend more than a fifth of his property (and perhaps less) to fulfill a mitzva.‎{&&8}‎ Most of these sources imply that if only an unpleasant reaction will occur, not actual sickness, which is usually described as being bedridden,‎{&&9}‎ one would remain obligated. To put this in perspective, one would not expend a substantial sum of money in order to prevent a mild headache. We find that one is supposed to push himself to drink wine‎{&&10}‎ at the Seder even if it affects him adversely.‎{&&11}‎ The extent of the effect of the wine and the question whether the drinking of wine is unique are discussed in the halachic literature.‎{&&12}‎ The question of how likely it is a reaction will occur is pertinent as well.‎{&&13}‎
In summary, one should not be reckless and need not be a hero in fulfilling the mitzva of matza if significantly adverse reactions are expected. However, one should look for alternatives‎{&&14}‎ and be willing to bear a fair measure of discomfort to fulfill a mitzva.