Thank you both. It's good to get advice from some real experts because I have a feeling my doctor would just be sympathetic but quite useless.
I like avocados and nuts, so I'll try having more of them. I'm in the UK and coconut milk, as far as I know, comes in tins with additives and sometimes thickened. Not sure if this is what you have in mind, but I will have a closer look when I'm in the shops.
Part of the problem is that I have been fine since I started the gluten-free diet a couple of years ago. I have got glutened a few times by processed food but it goes in a few days. So this is something new and I have to adapt to it. Perhaps I need to get more organised, as you say, and keep a track of what I'm eating, and also do an elimination diet.