Yes we do. Recombination and meiosis occur in people much the same as in pea plants.
Anyhow, as for allergies, they are caused when IgE (an antibody) cross-links FC-epsilon-RI receptors on mast cells, stimulating release of histamines and other effector molecules. From Immunology, 5e by Coico, Sunshine, and Benjamini:
The Protective Role of IgE.
The protective effects of allergic reactions may be seen in situations where the sensitizing antigen is derived from one of many parasitic worms such a helminthes. The immune response to these worms favors the induction of IgE. As a consequence of antigens from the worm cross-linking of IgE on the surface of mast cells (an eosinophils), histamine, and other mediators associated with the anaphylactic response are released. The effects of increased permeability due to histamine release serve to bring serum components, which include IgG antibody, to the site of worm infestation. The IgG antibody binds to the surface of the worm and attracts the eosinophils, which have migrated to the area as a result of the chemotactic effects of ECF-A. The eosinophils then bind to the IgG coated worm, by virtue of their membrane receptors for Fc, and release the contents of their granules (Figs. 14.8 and 14.9) As noted earlier, eosinophils also express the low-affinity Fc receptor for IgE, which facilitates the binding of these cells to IgE-coated worms. The major constituent of the contents of the granules released by eosinophils is an MBP, referred to previously, which coats the surface of the worm and lead, in some unknown way, to the death of the worm and its eventual expulsion. This beneficial effect of the anaphylactic response involving IgE may have evolved to play a role in dealing with worm parasites.