pre-note: the allergies are examples, as I'm not sure the specifics here.
The money you'd spend on just going to a specialist will far outclass what you are going to find online. They are able to isolate exactly what is causing the allergy and intolerance.
Personally, I don't think that food allergies are increasing so much as there is a wider understanding of allergies and intolerances (there is a difference). Conditions that were unclassified 20 years ago are now acknowledged as real conditions. Only a few years ago, people who would complain of being allergic to "hypo-allergenic" foods like bananas, plums, cherries, and so on were laughed out of the office and called hypochondriacs. Dust, pollen, and peanuts, and similar were classed as allergens. Today, the story is different. The relationship between seasonal allergies and food allergies is better understood. For example, you can be allergic to a certain tree, which only blooms in fall, and that tree will trigger a food allergy that only expresses itself during the fall. This doesn't mean you should start eating an allergen during the off-seasons (IMO).
I live with a lot of allergies and intolerances. My best advice is to simply stay away from what can make your daughters sick. Unfortunately, they will end up discovering allergies the hard way, and you can only support them by trying to recognize what is going to make them ill. If you open an orange and they are sneezing, stop buying and eating oranges. Everyone will have to make some sacrifices for them, but at the same time, learn to differentiate between what is okay and not okay to eat around them.
There is nothing more irritating than eating a piece of strawberry cake and apologizing to them for eating that in front of them. To them, you are eating poison, so it's no loss to them.
And FFS, please for all things lovely, don't ever ever ever sneak an allergen into their food to see what happens. That's incredibly rude, and yep, their friends and boyfriends are going to do this to them (ugh).
I will say that there are various reactions. For me, I know what I can and cannot eat. If I get something on accident, I'll simply toss up in about 15 minutes, which is much better than the reactions I used to get.
Please just listen to your doctor. Get the allergy shots, and get the epi-pen if needed.
I would also (lightly) advise that the issues with allergies is compounded because a lot of people don't understand nutrition at all. Adkins is good, bad, neutral? What? I'm nearing 40, have good general health, and look about 10 years younger than my age. I know of a few others with a similar range of allergies who are in amazing general health. A friend's relative plays professional sports and can eat maybe 10 things without getting ill. While it emotionally hurts to see someone who can't eat all the "healthy" stuff, just remember that it is poison to their body, and you just have to work with what you have.
Hope that helps.