I reckon you need to cut the tomatoes out - they can cause eczema and all sorts of skin problems including dandruff. Also try rubbing some pure organic virgin coconut oil on your skin, it is very healing (antibacterial, antiviral and antifungal). Are you taking a good multivitamin?.
If you occasionally eat wheat in the junk food, it may be that? Wheat can take 8 weeks to leave your system and for healing to start (my youngest was born allergic to it, so I've had a fair bit of experience with how long it can take. Not that I ate it often once we realised what the issue was, and never on purpose)
Some people have issues with the erythritol. I will itch for days if I have any exposure to gluten, and the longer I am gluten free, the more sensitive the reaction.
Sounds like a bit of eczema, which can be caused by a variety of things for different people. I used to have it all over when I was a kid but it has gotten a lot better as an adult. I have dust mite covers on my bed and pillow, clean my house with natural cleaners like vinegar and baking soda, double rinse my laundry and use a mild detergent, no antibacterial soaps on my hands and try to wash them mainly with water, Aveeno skin cream for my face and body. These things were all trial and error over the years but have helped a great deal.
The thing with eczema is that it's not always just one thing. It's a hypersensitivity to a number of things which can be both environmental and food-wise. Tomatoes tend to be my trigger food and will keep me up at night with an all over itchy feeling as well as cause cracks in the corners of my lips.
Good luck finding your trigger.
Have you tried anything like cortisone? If it is greasy and oily, I'd not be using anything like shea butter, unless you enjoy clogged pores. My other thought on dandruff and oil is salycilic acid. I get peels that use it (and other acids) and it turns over your skin cells and declogs pores. It seems counterintuitive but it works. An aesthetician could help you.
That sounds like an allergy or sensitivity. Try switching to something milder for everything that touches your skin. My brother developed a bad allergy to one particular brand of laundry detergent when he was in college. Did you change anything (soap, diet, etc) around the time you noticed it getting worse?