I would say that you would have systemic candida. Antibiotics wipe out all of the bacteria in the body within 5-7 days. That allows for candida to convert from its yeast to its fungal form. The skin will often reflect the health of the intestinal tract. The allergies will be related to imbalances within the bacterial flora of the body and possibly to fungal candida's effect on the immune system causing a shift toward allergic responses. The IgA shows an active immune response at the mucosal level on the intestinal tract.
Along with fungal candida and past antibiotic use, we usually see blood sugar imbalances and low levels of HCL in the stomach. Low HCL leads to decreased absorption of protein, iron, iodine, calcium, magnesium, Zinc, B12, folic acid, and other minerals.
Brain fog is usually a symptom of inflammation of the brain and body. Fungal candida drives inflammation in the body, and inflammation promotes the growth of candida.