Ouch, that does look sore!

When you say you changed foods, was that to another dried food? I'm wondering if it could be a grain allergy - My PON boy has similar lesions on his paws and round his mouth for a long time until someone suggested it could be a wheat (gluten) allergy. I changed the kibble to wheat-free which improved matters a lot, but now he's on raw.

Either way, I agree it needs a vet's opinion. If nothing else you need to have things ruled out and a skin-scrape might be advisable to rule out mites.

Ouch! Is it just on that one side?

Is it just on one side?

The scratching is worse on one side, but he scratches at both.

He only wears his muzzle at the vet, which he has only been to like 2 or 3 times, he is only 2 years old.

I am not sure a light sedative would work. They might need to knock him out. I really dont know why he acts like that. My nieces are over all the time and it took a while for him to calm and relax enough to let them walk in the same area. We had to block him off. But they still can't pet him, he will growl at them.

I was feeding Beneful, it gave them awful gas. Then switched to Purina One Smartblend. Then I did some research looking for an affordable no wheat food and switched to Pure Balance chicken and brown rice, no wheat no corn no soy. Still no improvement.

I really think its time to discuss with the vet either sending a picture or sedation. That looks very sore and uncomfortable and my worry is it getting infected.
I had a large breed who hated the vet he was always muzzled and when very ill and admitted sedated and while there for tests a period of 10 days he was sedated each time so it can be done and vets will know just how much to give him to stop him stressing and them getting bitten.
If it could be done with my 11 stone bernese it can be done with any dog.
So please at least send a picture if possible and get it looked at.

If it is allergy to grains, he could even be sensitive to rice, which most of the 'sensitive' kibble are based on.

Does your dog have bones or chew toys, and does he hold them more against one side of his mouth? I'm wondering if he could be allergic to something that he's gnawing on, as the reaction is worse on one side. Just a thought.

You could try Viacutan, this is a veterinary oil pump which you squirt on to the dog's usual food. It contains EFAs and reduces inflammation/allergic reaction, but expect to use it for 3 months before you see things improving - it takes a long time for allergic reactions to calm down whatever you do, but now Esau is no longer chewing and scratching (he's been on Viacutan for the last 2 years), and it used to be a usual occurrence for him to be in a cone-collar. Your vet can get it or you can buy it online - I buy mine from Amazon. It looks scarily expensive for an oil but one canister will last you several months. Don't bother with the capsules, they look cheaper but aren't in the long run.

Alternatively you could try coconut oil - I haven't used this myself but I've read it can help. Again, add to food.

Perhaps Camrosa mught be worth a try. It looks as though its 'contact' dermatitis or similar so def worth while look at other things he may chomp on.

Have you tried bathing it? If it were me I would try regular bathing with a weak hibiscrub solution dry it and apply sudocrem or something like camrosa http://www.camrosa.co.uk/dogs/dogs-itchydryskin/

Have you tried sudocrem? When and if you do use it, take him out for a walk after putting it on so that he doesn't get chance to rub it off or you could use hypercal cream. Wash in luke warm salty water first to remove any debri eg: dirt etc. As to food I would change to salmon and potato. Just make sure that the ingredients doesn't have rice in which vets kitchen does, I feed Fergusons salmon and potato.
Nelsons Hypercal cream is a first aid application that provides relief for all types of cuts and grazes
A topical herbal remedy traditionally used for the symptomatic treatment of cuts and grazes
It combines the natural healing properties of Calendula and pain relieving properties of Hypericum
Active ingredients: Calendula officinalis tincture and Hypericum perforatum tincture

Vets first and foremost, but just an observation, many dogs these days cannot tolerate chicken

The photo seems to show that he has lost his 'feeler' whiskers. Do you think he might have a follicular mite infestation?
Your photo is very clear, I think this, in conjunction with a light sedative and a basket muzzle, should be enough to enable a vet to make, at least an initial, diagnosis. In my experience they usually treat for the most common causes first anyway.