Hi, So I'll try and respond in the order of items you shared, but first I wanted to say your situation is really challenging with your allergies and sensitivities. I really feel for you and can understand why your stress triggers are mostly related to your chronic health issues. Please know I'm just tossing out ideas/suggestions hopefully some may help.
Casein/Whey issues and lactose intolerance - Mayo is high in calories (could choose ones made with avocado or olive oil) and you could have it with tuna, eggs, add it to mashed potatoes (yes, you read it correctly). You will want to look to make sure there is no casein in the mayo. Nuts and nut butters are loaded with calories and you don't need a large amount for the calories to add up. You can ground them up and add to other foods (oatmeal, smoothies (your Orgain drink blended with fruit), soups, noodles, sprinkled on fruit). Nut butters can/can't work for some so you can try different ones (sunflower, almond, cashew). Speaking of nuts, you could try nut milk (coconut milk, almond milk, cashew milk). Hummus is another item high in calories. Avocados are high in calories and can be blended into other foods/soups etc. Several of these items are also good protein sources. beans are good too (added to other foods, blended or whole if you can tolerate. Dried fruits are high in calories and can be eaten on their own or diced/blended and added to other things. Honey can increase calories too. I would suggest trying one new item at a time so if you have issues, you will know what caused it.
You probably already are aware of this, but just in case you don't, ingredients on products are listed in descending orders. You may find items you know cause a problem "sometimes" or always, should be as far down the list. That way the item will have less of them in it and you may be able to tolerate it. Keep in mind, your vitamins and supplements may have casein in them. You may find the liquid version of meds/vitamins are better tolerated and you may need less of them because the liquid versions are better absorbed. Not sure if you saw that I mentioned that I take Iberogast before meals. Not sure if you are willing to try because you are so sensitive, but you could take a small amount before one meal to start. Gradually, add to another meal at small amount, then to your last meal. Then, if needed you could increase amount.
I would definitely suggest meeting with a dietitian and a therapist (especially since you know stress is a trigger). I hope some of this helps. Take care.