The wine reaction could be sulphites. It is used as a preservative in most wines and it is known to cause a lot of allergies.
For the other things, I've been through soemthing very similar, and it's been a long road, but hopefully some of the things I have learned/encountered along the way can help.
The milk allergy could be a casein (milk protein) allergy- I had this, and the symptoms are blocked sinuses, stuffiness, puffy face, and also skin problems acne (face, arms , back). There is a lot of evidence emerging that coeliacs are much more likely to have a casein reaction than the rest of the population- casein and gluten are similarly shaped proteins. This can also means that the proteins in other grains (e.g. avein in oats, zein in corn) can cause the same problems as gluten in some celiacs. I find I'm only ok with white rice (preferaby jasmine rice) and quinoa. www.glutenfreesociety.org
Yes, it is a good idea to avoid things that you are mildly allergic to, for all the reasons A, B and C that you mention. Also it helped me to understand that underlying systemic inflammation in the body is what you really have to tackle. All the little and big allergic reactions contribute to this, and increase it, and so make it more likely you will have more reactions. It's a negative spiral but it is one you can reverse.
Chicken and duck are quite high in omega 6s, as are many vegetable oils. The wrong omega 3 to 6 balance can cause a lot of inflammation in the body, so restoring that balance can help a lot. That means a lot of fresh fish/seafood and maybe a supplement, plus reducing sources of omega 6 (so corn oil, rapeseed oil, vegetable oil) and switching to grass fed meat rather than grain fed meat if you can. However, if you have lot of systemic inflammation, you might also get into the territory of having histamine reactions a lot- and fish, seafood and meat are all high in histamine- and the histamine levels rise as the meat/fish etc gets older. So this means as fresh as possible and no frozen, plus finding an omega 3 supplement that is vegetarian source, preferably algae, rather than fish oil. The low histamine chef's blog is good on this. Gentle, not strenuous, exercise lowers inflammation too, as does managing other sources of stress, reducing synthetic chemical products (make up, cleaning materials, no fake foods). Being as organic and free range as possible does too. Getting enough vitami D from a little bit of sun exposure works too.
I can't have gluten and most other grains, dairy, eggs, nuts, lettuce, strawberries and any fodmap foods. It is really restrictive from one way of looking at it, but itis also really simple from another way of looking at it. So lots of fresh fish/seafood and rice are my staples, along with fresh herbs and green leafy vegetables. I can have chicken though, but would suggest lean grass fed beef and free range pork as alternatives. Also maybe look into lean wild meats like venison, they can be really healthy.
I now eat, basically white rice, white potatoes, coconut oil, olive oil, fresh fish, meat, game and seafood, herbs, spinach, rocket, lemon zest as the basis of my diet. Somethings that seemed really overwhelming has turned into something really simple and easy- since I focussed on what I could have and getting the best quality and freshest of that, rather than thinking in terms of what I can't have. Cooking is simple, quick and easy. I can sometimes have a small quantity of other fruits and vegetables, but a tiny quantity e.g. a tablespoon or two and not everyday (my safe list is blueberries, peppers, courgettes, . I can have a wee bit of dark chocolate once a week or so. I need to do 40 minutes of low impact cardio everyday- no more, no less. I avoid stress like the plague.
It's not cheap and it's not easy to get your head around. But when you do get your head around it, it is actually really simple to do in practice- I feel free of the constant obsession with food that our society has.
And you can get no added sulphite wine, so it is possible to have the occasional glass. And Chase make vodka/gin from potatoes and apples rather than grains if you prefer a spirit.
Good luck.