Hi -- let me ask a few questions and then I'll give some suggestions.
Since it's got the feet so sore (and you aren't saying belly or other parts - just **feet**) and then the mouth -- I'm thinking this screams contact allergy. How is the belly?
If it's on the feet and NOT the belly then I would tend to think it's something the dog walks thru himself -- if it was on the belly too I'd think it was something tracked indoors by a human and the dog lays on it.
Can I ask where abouts you live?? I don't want your address -- but where you are located geographically? City/country? Do you have grass you walk him thru?
Do you happen to have any wandering jew?? In some places that's a plant in the house (green & white striped hanging plant usually -- very common - little leaves that are striped from stem to tip of leaf). In other places it grows wild outside and there are tons of varieties -- the outdoors 'wild' one tends to be an all green leaf -- likes to creep on fences, walls and in other bushes. There's also a red/green varigated one that is very very hardy and in southern/warmer states landscaping companies love it as ground cover - it actually appears *purple* but often it's planted at the base of trees, near doorways -- anywhere someone might walk off a 'corner' of lawn.
Wandering Jew in all varieties is a serious irritant but if it's outside your house -- the dog doesn't have to set a toe in it -- just the oil from humans walking thru and bruising a leaf or two and then walking IN THE HOUSE -- the dog gets it from secondary contact on the carpet.
Other serious contact allergens (think poison ivy to us -- that's a contact allergen that bothers humans but dogs actually have way more of them). Poison oak, night-blooming jasmine, and St. Augustine sod (not the whole sod -- it's a couple of little weeds they have introduced into the root system that help hold water which is why St. Augustine sod is so hardy).
Once the feet are totally sore, then yeast or staph sets in -- but even if this was cultured, you may discover the secondary stuff on the skin like the yeast or staph, and the original irritant can go undiagnosed.
But often when a dog licks a sore area *trying to get the stuff OFF his feet* then the muzzle gets sore. On a doxie it would be hard to tell but are his 'lips' (literally the very edges of his mouth) sore looking??
Remedies:
Like I said to a degree you may have to treat the top of the skin to reduce the whole problem until you can address the whole issue.
1. If it's yeast (and that's not a bad thot -- wet, moist, area kept wet by the licking will grow yeast) the Selsun Blue is a good idea (my vet has had me do that many times) -- just don't leave it on the skin long and rinse SUPER well. Dilute the shampoo first or it will clump on the skin.
2. If you suspect the contact allergen -- any benzoyl peroxide shampoo is a good idea. OxyDex or Benzoyl Plus are brands you'll find at the vet and online. Oxy10 Facewash (which has just been re-released in a black bottle) in the teenagers acne section of the drugstore or grocery store -- again seriously dilute it before putting it on.
3. IN ALL CASES -- whatever you wash the dog with (and I'd do the WHOLE dog -- so the oils of whatever it is can't spread) do a final rinse in tea tree oil and water -- about 1/4 teas. to about a gallon of water. Stand the dog in a dishpan and add the tea tree oil to the water and then use a mug to pour cupfuls over and over and over while he STANDS in it. It will help heal the paws and help with the itch.
4. Aloe -- don't use a commercially prepared aloe and NO lotions. You want pure aloe, literally you want an aloe plant and you can harvest the goop out of the leaves. Very very healing.
5. Put baby socks on his feet if you have to but keep him from licking. He doesn't need to ingest that stuff and you don't want him licking off any of the above either.
Most effective -- when you see him lick, gently say "oh baby, no licking! let Mom help" and go TO him and massage his feet very gently. But it will effectively 'scratch' the area and relieve his distress. Even if you do that 50 times in the next hour -- don't let him lick. He will learn "no licking" as a command and he will also learn to come TO *you* and that you will 'help' him.
6. Another good soak (and you can do this several times a day) is chammomile tea. It's a good topical anti-inflammatory. Lavender oil (just a few drops) in it is also a good addition. You can put this in a spray bottle and actually spray it on.
7. Add chammomile to his food -- just make the tea bags like it says on the box and just about every grocery store has chammomile tea in the tea section. Don't throw away those soggy herbs - add them to his dinner -- they will help settle his tummy and they will help reduce the pain from the inside but they aren't hard on the stomach. Chammomile is a mild NSAID like aspirin, but totally *without* irritation to the stomach -- instead they actually help settle the stomach.
Often a vet is not going to catch a contact allergy like this. But I strongly suspect there is something external causing this. And it could even be a spray someone puts on the lawn!