From what you describe it sounds as though your boy has folliculitis. The black spots on the tummy are what we call "black heads" in people. Also the bumps on the back would be follicles that are plugged with debris. If there are no other skin issues (except the nasal fold ones) I doubt this is a food issue and would look elsewhere.
One thing I would definitely consider doing is a thyroid panel blood test. One of the most common signs we see with hypothryroidism is skin issues. Take care of the thyroid and the skin clears up!
Another thing to try is a follicular flushing/antibacterial shampoo. It helps to open the follicles, get the debris out, and clear up infections. Generally, I don't start these dogs on systemic antibiotics until we've tried and failed with topicals.
If a skin problem is refractory to treatment, I usually recommend a skin biopsy so that the pathologists can give us an idea of what is going on at the cellular level.
Finally, as it is so cold and we have the heaters on, I generally recommend getting a humidifier going and putting some moisture back in the air. We are all suffering from dry skin right now. If you don't have a humidifier, consider putting you pet in the bathroom during shower time or with a tub of steaming water.
I hope this helps and gives you some ideas to discuss with your vet.