An oddly shaped question indeed.

Both beta, and alpha pinene are irritants to the mucosa, and beta-pinene is toxic according to their MSDSs.

Alpha -pinene is what makes your eyes burn if you rub them while trimming.

However, they have nothing to do with pine nuts, so a pine nut allergy is irrelevant.
In short, relax, it's not a problem.

Aloha,
Weezard