It does sound like a dairy intolerence, esp with the eczema -
Oatly is the oat milk - the red one has added calcium, the organic one doesn't
Vitalite and Pure sunflower are both dairy free. I used the marg and milk for cooking etc using "normal" recipes. ReadyBrek (or the supermarket own - pretty sure they are all readybrek!!) is a really good source of calcium.
I would get your dr to refer you to the dietician so you can get some advice, but if not I can tell you how I did it with M (through advice of dietician) around the same age. The dr prescribed Neocate to ensure he was getting enough of everything, so you could ask your dr for it (with O I just asked for Neocate and even had to spell it out!).
posted same time as last 2 posts! M's stool used to be like cake mix when on dairy/soya !!