Most kids grow out of fussy eating, so really no need to waste the time of the GP who can't do anything anyway, unless there are actually some physical problems being caused by it, i.e. severely over/under weight.
Our son was an absolute nightmare. He didn't even eat his first chip until he was 12. He refused fresh fruit and veg. It was all yoghurts, billy bear meat sandwiches, and tins of beans/sausage for many years! In his teens, he "discovered" McDonalds, and would eat a burger and chips there, and then went onto hot dogs and pizzas, but it was still mostly processed crap, and he'd still refuse fresh fruit/veg, "real" meat, etc throughout his teens, and would pick off pieces of meat off his pizza etc.
He only changed when he started at Uni. His flat mates started making jokes (in a nice way, not a bullying way) about the food he cooked in the communal kitchen, i.e. tins of processed crap all the time (baked beans, beans & sausages, all day breakfasts) and frozen pizzas, and when he went out for meals with them (or had lunch out with them), it was always simple sandwiches or pizzas etc.
One day, he just kind of "switched" and started eating everything. His first Christmas home from Uni, we gave him a full Xmas dinner and he just ate it all, including real meat, all the veg, etc. Ever since, he's like a human garbage bin and will literally eat anything at all, happily eating roast chicken, pork, lamb, etc., and looking at his fridge and cupboards in his flat (now living at the opposite end of the country in his first proper job), not a tin of beans in sight, a fruit bowl full, veg tray in the fridge full, etc.
I think you can over-think the eating "disorders". We were really worried through our sons childhood, right up to Uni, and both he and us were worried about his eating when he started Uni, but something just switched in him and he turned "normal" virtually overnight when he was living amongst his own kind!
My advice would really not to make a fuss, just let them be, let them eat what they want (as long as it's not ridiculously unhealthy and causing weight gain), and they're more than likely to grow out of it.