So, a few questions. First, you mentioned your skin is too sensitive for skin prick tests. Also you mentioned severe anxiety, and multiple deficiencies, which are suggestive enough to ask a few questions to see if you have reactions that better fit a mast cell disorder profile than a standard allergy profile. (two closely related allergic disease types)
First, do you get reactions to things that don't fit well within normal allergies. i.e. any of the following:
reactions to sunlight, exercise, heat or cold, stress (physical or emotional). strong smells (particularly perfumes, soaps, cleaning chemicals)
Also possibly relevant would be a family history of high flexibility, joint pain, with or without elastic (stretchy) skin. (ehlers-danlos syndrome)
Things to know: first, if you have had IgE blood testing, and it's positive, that DOES indicate a food allergy so long as you have symptoms when you eat those things. That isn't really subject to debate. If a food triggers symptoms, you need to cut every last trace of it out of your diet. This could easily require cooking everything yourself and not eating any more fast food when it's something as ubiquitous as corn. For lower IgE numbers (less than 2 or so) you might want to get a second opinion and a second test from another allergist.
corn syrup is in nearly everything. soft drinks, ketchup, barbecue sauce, etc. Corn starch is added to many things you wouldn't think have it. Like powdered sugar and some grated cheeses. So read all packages. Soy is also in pretty much everything, however many people with a soy allergy can tolerate soy lecithin and soybean oil. so you definitely want to discuss that one with your allergist. as if that can be safely eaten it expands a LOT of prepackaged food.
Rice makes for a wonderful base to get your starches/carbs in. you will also find it's common in gluten free flours. Cornstarch however is also common, so you will need to read any premixed flour recipes to ensure it's not present.
https://minimalistbaker.com/diy-gluten-free-flour-blend/ that's a flour recipe that is gluten free and cornstarch free. It does contain some potato starch, which I'm uncertain enough about PCOS to be sure as to if it's something you need to avoid completely, or small amounts are fine.
Meats, veggies. homemade sauces work well for meals. Here's a corn syrup free ketchup recipe
http://allrecipes.com/recipe/232397/homemade-ketchup/you can also use homemade ketchup like that as a base for barbecue sauce. (google recipes on this one, most involve adding liquid smoke, paprika, chili powder, cayenne pepper, mustard powder etc to ketchup)
so for instance, in the morning before work, you can baste some ribs with barbecue sauce, slow cook in a crockpot on low, then make some rice and say broccoli or asparagus when you get home and have the time consuming part (the meat) done well before you get home. slow cooked and tender

You can bake your own buns for hamburgers with gluten free flour, (assuming it's something you can eat) and then freeze them. when you plan on making hamburgers, simply move them to the fridge in the morning, or the night before, and they will be defrosted enough to crisp up nicely on the stove when you want to cook hamburgers. (see above ketchup recipe)
I hope this helps give some ideas.