Anyone educated in nutrition/allergies?

From personal experience I would say get an allergy test done on the dog. 

If it is in fact food allergies you could pull your hair out trying to figure out the one thing the dog is allergic to (my Aussie had chicken allergies, switched to a lamb formula and all was well, but many foods had chicken further down the ingredient list). Not just main ingredients count and if you know what's setting the dog off you can research foods better based on what you need to avoid on the ingredients list. 

There are also allergies other than food that could be causing it. If the dog is suddenly showing symptoms and you haven't changed food that makes me believe it is not food related. Anything change in your home recently? New blankets? New decoration? New plants? Anything that has changed in the home could be what set it off. It could be something as simple as a seasonal plant in your yard that may have not shown up the last year or two. 

I would argue it's going to be a lot less stressful to you both to pay the money for the test (note that the skin test is a lot more reliable than the blood test). If you still want to try different foods I would suggest finding a quality brand and trying different formulas of it one by one. Remember when testing a food you can not have any extra treats or snacks until you are sure the food is not causing an allergic reaction. 

I wouldn't rule out the option of speaking to another vet either. If you're vet has told you your dog has fleas when the dog has no signs of fleas there's always the option of getting another opinion. Fungal infections and a variety of skin issues can be caused by more than just allergies.

There seem to be more thumbs-down trolls than responders interested in your question! A couple of others have summed up some of the band's history, so I won't go too much into that. From a musical perspective, Floyd is a fascinating band because they were Prog Rock in many ways, yet showed remarkable restraint in their arrangements - the only player who would really take off & fly is David Gilmour with his phenomenal solos and sonic textures. Perhaps because Waters was so focused on controlling the band, there are very few songs with riffing bass lines - almost the polar opposite of Entwistle's blazing bass with The Who. So The Floyd is generally not a 'virtuoso' Prog Band like Yes or Emerson, Lake & Palmer; yet, the band's music gradually developed in sophistication after Gilmour joined the group and Waters became the dominant songwriter. The Meddle album is underrated; it features the epic-length "Echoes" which brilliantly captures many facets of the band. Dark Side of the Moon is, of course, justly world-famous. Wish You Were Here is seen my many to be somewhat flawed, but in its day it had the disadvantage of having to follow Dark Side, and would inevitably suffer in comparison. But the album is noteworthy for the brilliance of Shine On You Crazy Diamond, and my favorite track, Have a Cigar, with a unique change of pace by the band: English folk singer Roy Harper handles the vocals. His performance is a beautiful match to the mood of the song.

I haven't had problems with THAT bad of allergies, but my Lab used to get terrible dandruff. She looked like she had just come in from playing in the snow it was so bad. I switched her on to Wellness Core and it solved it in about a week. Her coat was WONDERFUL. No dandruff whatsoever. Eventually I switched her onto a balanced RAW diet and her coat got even better. It got a lot brighter and shinier. Unfortunately I've had to recently stop feeding RAW do to the fact I just don't have the room or time for it. But she's back on Core and I've still had no problems.

It is a bit pricy, but it makes my girl look healthy and even the vet compliments her coat.

Buddy is a peekapoo. the vet put him on IAMS lamb & rice for his allergies and he is so much better. No more scratching his face on the carpet or rolling around scratching his back either. The fact that you don't find fleas doesn't mean they are not around. Try K9 Advantix for a while. Or it may be mange.