Well, yes and no. Parmigiano Reggiano is made with raw milk. They innoculate the milk with the whey from the previous batch. So essentially, a long time ago they would have soured the milk naturally and made cheese from it. Because parmesan is heated to 55 C during the make process, only a very few bacteria survive. They put the whey from that into the new milk and repeat the process. Over time, the whey builds up this bacteria that can survive 55 C (which you can buy -- it's TA61 from Danisco Choozit). But it's just a particular strain of strepocarpus thermophilus (ST). ST (in various strains) is the main acidifying culture for literally every thermophilic yogurt on the planet. It would be *really* weird if you were allergic to a single strain of ST and not to others (not to mention that TA61 is often used in commercial yogurt as well). If I were to guess the problem you are having it would be histamines....
What I recommend is to pick up some TA61, make yogurt from it and see if it causes problems. If not, then do a parmesan recipe, but eat it young (like after a couple of weeks). If that's not a problem, then make one and age it for a little longer. Finally, try aging one out to over a year. My guess is you will have no problems unless you age it out to 1.5 years or more, so that would allow you to have a decent parmesan style cheese. It won't be as good as real Permigiano Reggiano (it's a difficult cheese to make at the best of times and it benefits greatly from making a large size -- which is not really feasible for the home maker). But probably you can make something that is very good with practice.
