Hi there! Dr. Hurst here.
This may indeed be an allergy. The skin turns red and warm when it is irritated. It can also turn black if the irritation is long-standing.
The skin may also react this way if there is an infection with bacteria or yeast. If there are pustules and/or a sour or bad odor, an infection may be the culprit. If the skin is merely red and itchy, there may be an allergy.
Allergies can be frustrating because it is sometimes hard to find the triggering agent. Dogs can have allergies to fleas (even one flea bite), foods or treats they ingest, or any number of environmental allergens. Inhalant allergies are often due to tree and grass pollen, mold spores, house dust mites, etc. Sometimes they can be caused by something the dog is in contact with, such as a new bed or carpet, new mulch they lie in, etc.
You can have allergy testing done to see what they are allergic to and even do allergy injections to desensitize them to whatever it is they are reacting to.
Symptomatic treatment may include soothing shampoos (every few days with cool water), topical ointments and sprays, and oral antihistamines. In severe cases we sometimes use steroids, but these should be a last resort due to the many nasty side effects. Of course, if an infection is suspected, an oral antibiotic or antifungal may be in order.
If your dog is only mildy uncomfortable you may try some aloe and oatmeal shampoo with cool water every few days. You can also give Benadryl at 1 mg per pound of body weight every 8 hours. This may cause drowsiness.
If there is an odor or if he is really miserable, you may need to have him in to your vet for diagnosis and stronger treatment.