Pygmy goats are like any other animal, if your pygmy goat is sick, you are able to give it some kind of medication (low does, of course) that is able to cure a type of cold. Just watch for the doses.
You will need to go to the vet and get medicine to give the little thing. He or she will also have to be kept in a warm, dry place and given food with a high nutritional value as well as some warm milk to drink in order to keep off a chill.