No! No! - not almonds or anything to do with nuts - not for a child who already has eczema!
If she is allergic to petroleum products then that rules out all baby oil, oilatum, petroleum jelly (aka vaseline) anything mineral based. Read the ingredients of all products and avoid petroleum products/mineral products.
Marigold cream is good - make sure it doesn't have anything else in it. Aqueous cream can be good, but always do a 48 hour patch test with any product - much better to get an allergic reaction on a tiny patch than all over.
I have had very good results with a specially made aromatherapy oil mixture - made up for me by a qualified aromatherapist.
I used aqueous cream in the bath and on dd's skin for about 7 years - she was allergic to everything else. Also - I washed her gently with my hands,(not flannels or sponges) and never used biological washing powder of fabric softener on towels or her clothes.
In the last year or so we have progressed to baby E45 bath stuff and that has been fine - she is now 9, and only has the eczema on her hands, and the odd patch on her legs and feet. Still can't use soap.
That has been my experience with dcs with asthma, eczema and allergies. They have all improved as they have got older.
HTH - good luck.