Hi Casa,
Ninja and garlic have already been great in their responses so sorry if I am just repeating things.
Eczema is definitely related to allergies, especially when eczema appears in the first few months of life. The theory behind this is that if you are exposed to food through the gut first then you don't develop an allergy, but if in the first few months of life when your immune system is so immature food crosses through the skin because of eczema, then you have a potential to develop an allergy to it.
Secondly eczema does flare up with food allergies in a large number of people, I suffer from eczema as does my DD and we both suffer from flare ups from certain foods. However not all of these foods cause an immediate allergic reaction in my DD, and definitely not in me.
Tests help in giving information but they are not conclusive, the only way you can be sure is after your DS has actually been exposed to food. So for example my DD had an anaphylactic reaction to peanuts at 9 mo, the skin prick test when she recovered was positive. She had another anaphylactic reaction to eggs after negative skin prick and blood tests to eggs a couple of months later. And she still tests negative to eggs. But it is very obvious she is allergic them and we have been told to avoid them. And she has tested positive to white fish which she can eat without any problems! As with lots of things in medicine, what you say and have seen counts for much more than what tests show.
The 6-12 month stage is unlikely to make much difference, the current evidence thinks it's the first 4-6 months you can attempt to make a difference, and a lot of that is with strict eczema management to keep the skin barrier healthy and intact. After 6 months it's unfortunately a matter of wait and see what happens.
Although your DS' symptoms to sound mild, the nurse is wrong to say that your DS should have failure to thrive to be urgent because that is really the extreme case scenario you want to avoid. The problem is as garlic has said that there is a huge demand for allergy services, with a huge cut in funding over the last how many years, and is about to get worse.
Where abouts do you live? I'm only asking because we are based in London and I spent a long time researching the current specialist my DD is seeing, have seen three other specialists who were pretty much useless and actually made things worse. By the time we were seen, and dismissed by other health professionals, my DD had gone from the 50th percentile to below the 0.4th percentile, her eczema was awful, and she was vomiting at least once a day with food and choking and gagging all the time with food, plus a lot lot more. So I can completely understand you don't want to get to that point before you're seen, because it is far better to avoid all this if you had the opinion of a proper specialist.
Anyway in case you ate based in London, we see Dr Helen Cox at Queen Mary's hospital Paddington, but she also does private clinics at Harley street.
For a private referral it is easier if tour GP can do a referral because they should include in the letter any useful background, and then the private doctor can write back to your GP with appropriate advise including any medications/dietary prescriptions that they can prescribe at a much cheaper cost to you than private prescriptions.
Sorry for going on so much, HTH! :)