Baby Allergies – Advice on Some Ingredients?

Hi! My 8 month old son recently had a reaction (hives on his face, neck, and hands) to yogurt, and also to a Nestle infant cereal that had skim milk powder, palm oil, and coconut oil. At first I thought it was a dairy allergy, but then I remembered he can drink formula with no problems, and he can also eat Mum-Mums, which have skim milk powder. So I’m not sure what it was in the Lil Ones Baby yogurt that affected him, and I’m wondering if it was the coconut oil in the infant cereal… anyways, long story short, I’m wondering if anyone out there has had similar issues and if you know if “coconut oil” would be considered a “nut”? My husband has a nut allergy, and my DS also gets eczema occasionally.

I bought some Arrowroot cookies today but they have Palm Oil so I’m a bit nervous about it.

Thanks!