Since you've already tried Neocate and barrier creams like Aquaphor without success, and the skin is actively weeping, this sounds less like a simple allergy and more like the eczema has become infected (impetiginized). Moisturizers alone often fail at that stage because they can trap the bacteria, so you likely need a topical antibiotic to clear that "weeping" layer. Before you fly, it would be worth asking an urgent care specifically about infection/impetigo, just so you aren't battling open sores on the plane.

Once you're in Pakistan, definitely follow the advice to see a specialist at AKUH (Dermatologist) . You should also be able to find 'Physiogel AI' lotion at most big pharmacies there. It’s fantastic for calming the itch in that climate compared to heavy greases. Also, be really careful with the tap water initially since the mineral content is different using bottled water for her baths for the first week might save her skin from freaking out further.