Dogs can have allergic reactions to vaccinations or immune responses to them. An allergic response will result with the first few hours after receiving the vaccination. They may develop hives, facial swelling, vomiting, diarrhea, high fever, and lethargy. If this occur an antihistamine and a trip to the vet for a steroid injection is recommend. Allergic reaction can become severe and life threatening.
An immune response can be triggered which can result in a low grade temperature, lethargy and in some cases soreness where the injection was given. Most dogs have mild symptoms which resolve on their own within 24 hours. Usually no treatment is necessary.
In some breeds like weimeraners a different type of vaccination is needed because their bodies react adversely to a particular part of the vaccine. These are special cases though.
If your dog is showing severe symptoms of illness following a distemper vaccination then I suggest taking him into the vet to be seen today.