No. I described at a high level just one of the mechanisms of adaptive immunity--one of the most incredible biological systems in my opinion. (Runtime metaheuristics search!) These are complex pathways that involve many genes.

If the system isn't working you probably won't live very long. And while there may be certain functional alleles that may increase odds of an initial false positive stimulation, by in large the entire class of failure known as "allergic reactions" is simply a result of how the system itself works. You don't really need to invoke genetic differences to see how it fails. This is why the hygiene hypothesis is so strong.

There are actually four major categories of hypersensitivity that involve different cell populations and signalling pathways (eg. why poison ivy allergy is different from pine allergy).

If you're interested, the Wikipedia articles aren't a bad read. I also recommend Janeway's Immunobiology as a great intro to the entire subject.