He has what is called infantile eczema,which will come and go till one year of age. Apply elovera cream twice a day and use a mixture of equal parts of glycerin mixed with equal amount of rose water or lime juice after every bath,daily. How did you discover nut allergy at this age?? If indeed he's allergic to nuts,they must NEVER be given,through out life. No tests are needed,it's an individual observation.