Oilatum is not always the best thing. It can cause problems in some children. You can try Balnaum and see if that helps.
My son also has severe atopic eczema. He has it about as bad as you can get . We have some control now (he is 6).
As you DS is atopic I would suggest housekeeping tactics to help manage his condition.
I hoover at least twice a day with the windows open. Damp dust daily. Hoover his bed everyday and dont forget underneath.
Try not to store anything under his bed.
My DS does not have any soft toys in his room and no carpets, rugs or cushions. He has blinds.
I wash his clothes at 60 and only use non bio (no fabric softener). He only wears his clothes once before washing. He changes as soon as he gets in from school because of the dust/pollen on his clothes.
I now use 'Method' cleaning stuff. It hasnt got any nasties in it and actually works so I think its worth a go.
We also have a strict skincare regime. We have got used to have a methodical routine and he never misses his cream/ointments etc.
Cotton clothes only - no synthetic.
Its a bit of a military operation but its the only way we can keep him the way he is.
Its not a cure but at least he is not bleeding and infected all the time anymore.
He has been on a course of oral steroids. They worked like magic and gave him a break. It was the first time in his life he had normal skin. The eczema came back but it has never been as bad. It gave us a fresh start IYSWIM.
My son is allergic to lots of things that we can not control so we have to try and manage. He is not allergic to diary or eggs etc. My friends DS was so allergic to milk she couldnt even have a latte when she was Bfing! I wouldnt have believed it unless I saw it.
I am sorry you and your DS are dealing with this. I used to be in despair.
I can only suggest what we have learnt over the last 6 years. It may work for you too. I really think my best weapon is keeping dust, dust mites and pollen away.
So sorry - loads of cleaning and washing .
BTW there are loads more things the doctors can try. There are quite a few new non steroidal treaments on the market plus medicated bandages (messy but work really well for us), different moisturisers (we use Epederm), different clothing/dressings.
Good luck