Believe it or not, most allergens to food develop after the age of 2. And they can also develop seasonal allergies as they get older as well.
Hugs to Chums.... Remember his reaction to those shots months ago? They could have also done some damage to his immune system permanently too. With these guys you just never know.
My vet told me each season they go through will depend on their reactions to the season, and wheather they have the anti bodies to fight the allergies or not. This is why most puppies with allergies are certainly having a reaction to food or household allergens, because they have not been through a season yet.
His coat looks like it is dry + coarse.... and see how the hairs are standing? The circles of dry spots could be ringworm, staph or just a dermitisis of the skin. Does his skin look "off" in color? Like "grey-ish"?
Also how long have you been mixing all the oils? Perhaps stick with just one oil at a time, there is really no benefit to mixing them all up, except yet another possible allergy to something.
Let me know if there is anything I can do to help, try NOT to treat this with antibiotics if you can. Using external meds and creams (panalog, douxo, malecetic, mediacted shampoo) on it and letting it run its coarse is the best option, unless he starts to become very itchy or it gets worse. I would have a skin scrape done just to rule out mange or ringworm.