To think my baby is allergic to all food?!

[Bluepolkadots42]

DS is a bit over 7 months old and we've been weaning since 6 months. He was combi fed breast and formula for 6 months but is now totally formula fed. No history of skin issues in family. Eldest child is fine. We took him swimming just after 8 weeks old and he came up in eczema like patches afterwards which took us over 3 weeks to sort out. I tried numerous different moisturisers etc. Eventually oilatum sorted it out. He's been swimming again a number of times since and no further issues as we apply oilatum before and after swimming.

Occasionally he will get mild dribble rash on chin and under neck as he is quite a dribbly baby.

Since we have started weaning however he has a permanent rash all over his neck and chest/neckline. It seems to go down overnight and then flares up during the day. This morning I noticed it hadn't gone down at all on his neckline and has continued to get progressively worse as day has gone on. See pic. He has also had patches come up on his inner wrist and cheeks too where food has made contact with the skin.
For the last 4 days I've been smothering his face, neck, under chin and chest and inner forearms with vaseline before every feeding time. This has definitely helped his face but the rash on his chest has never been so bad.
A typical food day for him is:
Porridge- either oats made with semi skimmed milk or baby porridge from cow and Gate. Served with banana or stewed apple or mashed berries.

Lunch- some finger food like cucumber sticks or melon and then mashed broccoli or peas. Maybe some Greek yoghurt if still keen.

Dinner- mashed sweet potato and carrot, Greek yoghurt and fruit like Berries or banana or stewed apple (whatever he hasn't had earlier in day).

Today he tried some scrambled egg at lunchtime. The chest rash was already bad prior to him ingesting egg.

Has anyone got any advice on what to do? Or experience of this? Did your baby grow out of it or is this confirmation he has an allergy or intolerance or just very badly prone to eczema?!
His skin reacts to everything from cucumber sticks to satsuma juice. There doesn't seem to be one thing that triggers it.
We wipe him down with just water on a flannel after every meal.
He is bathed properly 3 times a week with no product in water then we apply oilatum.
I'm applying oilatum to his face, chest, chin and under chin every night atm.

I'd cut out eggs- I don't know what the current recommendation is, but when my DC were young, it was no eggs for babies under 1 year old. DS3 had eggs around that age and developed a hive- like reaction straight away. By 3 it wasn't a problem, although he does have mild eczema even now as an adult.
Cows milk and citrus fruit are known triggers, so pending medical advice I'd avoid those too, along with anything that can colour your skin- like tomato, mango, strawberries .
I've read that pears and lamb are amongst the least allergic foods, does your DC react to those? Might be worth trying.
With my DS, his eczema is also triggered by wetness, so dribble and sweat are things to watch for- we used only cotton materials next to skin and kept him as dry as possible. Chlorine in swimming pools was a problem- we moisturised before and thorough shower and moisturiser after. Being in wet clothes was/ is still an issue, which had sadly ruled out certain activities. Even sitting on the floor cross legged at school could trigger sweaty backs of knees and another flare up.
Unfortunately I don't think skin issues are well understood by the medical profession as a whole, and it's often trial and error trying to figure out what helps.