Since you have a family history of allergies, and since all sorts of intolerances can make it harder to live in one's body comfortably, these could definitely be related. And something of a vicious cycle can get established where physical discomfort leads to mood changes, which lead to unsatisfying interactions with the family (punishment), which lead to further mood changes which lead to physical symptoms. The skin, digestive system, and lungs are all prime areas where emotional upset can create symptoms, and so allergy and stress can be hard to tease apart.
It would be a great idea to get her tested for other food intolerances (gluten is a common problem). Also consider bagging up most of the household cleaners you may be using and trying non-toxic alternatives (baking soda and vinegar are great!) for a month: unscented laundry detergent, vinegar for fabric softening, no air "fresheners," avoid disinfectant sprays (many toxic ingredients, and they don't work better than a wipe-down with white vinegar). I have severe chemical sensitivities and have watched calm children have amazing meltdowns in group testing situations, just moments after a diluted drop of some common chemical was squirted under their tongue).
Because of her age, the behaviors are probably at least partly age-related. Strong discipline can be too over-the-top for toddlers who have very little impulse control (especially if they are tired, hungry or sick), desire *everything* but are too young for most of it, are infuriated by punishment and control, tend to be rigidly scheduled, and are in the two most frustrating years of their pre-adolescent lives.
There are peaceful, empathetic (but still firm) parenting options that work better for many children, and I have yet to meet a little who has been harmed or spoiled by these alternatives. Google "emotion coaching," check out http://www.askdrsears.com/, read The Happiest Toddler on the Block (and in another year or two, How to Talk So Kids Will Listen, and Listen So Kids Will Talk) for more on how to parent (most) children with little or no "classic" punishment. Fantastic stuff.
My best to you. I hope you get to the root of your daughter's troubles soon.