5 yrs old girl with high eczema and dry skin not healing [urgent help needed]

Hello if anyone has any remedy suggestion please help. Below case details

1. She will be 5 yrs old on Oct 3 2020
2. Slightly lager for her age. Not chubby, but strong built. Very atheletic, sporty and felxible.
4. Normal around new children and like to interact with adult males specially. Very stubborn, spits out food which doesn't like, does not eat fruit at all. Very limitted eating choices. Loves milk. Energetic, very angry, does have speak properly yet. Learns by watching, doesn't like to be instructed. Loves her mother quite a bit.
4. Have speech delay. Does not talk proper sentences yet.
5. At this stage bad eczema and very dry skin. Recovers from sickness very quickly and does not get sick easily. Had very high jaudanice when was born, needed blue light therapy. Was born very thin.
6. Just lotions make it temporarily better. Have to try multiple things as just one thing does not work after few days.
7. Cold weather, maybe clothes, does not like to put on cloths in house, scratching, dry skin. Likes to be in Sun not matter how hot it is. Does not like sweaters in cold temperatures. Also anger seems to create rashes.
8. She scratches, often to bleeding. Almost never cries, very high threshold to pain. Very reserved as a kid.
9. Born with dry skin and high jaudanice. Eczema is really bad on elbows and behind knees and ankles. Gotten really worse this year and is not going away. Until last year it was regular eczema that would go away as soon as alergy and dry season is over.
10. Alergy, diet, body heat
11. Thirst and appetite not very great but may be ok.
12. Eat junk foods.When she was 1 yr old she use to eat everything. Now very limited diet and loves milk. Puts lot of stuff in her mouth like oil, paper, soap etc. Tried child proofing but will find something to put in her mouth other than food.
13. She does not like anything new or does not like fruit at all. Will spit it out if does not want to eat. In most cases.
14. Loves choclate powder milk.
15. Urine normal. Stool always constipated and not regular bowls.
16. Sleeps two times a day but not regular pattern. Resist sleep a lot. Previously was light sleeper when less than 4 yr old. Now much better.
17. Almost nothing but scared of tigers.
18-19. She doesn't sweat much. Most often head while sleeping.
20. No problems up until 4.5 yrs of age. Had cold and runny nose very rarely and lasted only 2-3 days.
21. Very hot. She does not feel cold even in winter time with 45-50F outside. Does not like cloths at all in summer and won't wear any jacket or sweater in winter.
22. Planned pregnancy.
23. During pregnancy mother had to take antibiotics for , no proper nutritiion, not paid attention to self due to first kid was 4 yrs old. Father was occupied with job.
24. Mother in father married for 10 years, strained relationship.
26. Father has genetic asthema and behavioral problem, food intolerance. Mother has skin problem and relatively healthy overall compared to Father.