Just returning to update on my status.
TLDR: Wrong diagnosis from almost every doctor (even TCM) I went to, ever.
My suggestion is to put the diagnosis of the doctor to the test. I can only input info based on my circumstance.
I no longer show allergy symptoms to egg yolks. After consumption it usually leads to skin bubbles on my palms, a lot of itching and scratching and scaly cracked skin.
Found out that I am not suffering from eczema, but the hand version of athlete's foot AKA fungus infection. Bought salicylic acid (in alcohol solution) and used for a few months now. Palm side is mostly back to normal skin, finger backs and nails still needs some time to recover.
If you recover using the below methods, congrats it was just fungus. If not you can still try using emu oil, can buy from the box rental shops (some of the chains, not all carry it). I did suffer from eczema recently, on my shoulder. Emu oil got rid of it.
1) Use the Salicylic in alchohol solution (can be bought from TCM pharmacies) on the affected areas. see if there is skin peeling and improvement after a few days.
2) Soak affected area in vinegar for 10 mins , pat dry then soak in baking soda for 10 mins. Repeat for a few days, see if there is improvement. Use cotton pads if affected area is not suitable for soaking (e.g Shoulders, face area)
3) keep affected area dry. can wash of course, but must pat dry asap. Fungus likes moist environment.
4) if there is damaged skin due to scratching or injuries, use vaseline on it. It promotes healing and acts as a shield against fungus invasion.