it is unlikely to be auto immune in nature.
autoimmune problems generally are serious disorders starting with fever
, weight loss
they may involve rashes but rashes are generally photo sensitive, the cold hands and feet may be a feature of autoimmune disorders
but they are generally associated with raynauds phenomenon which is a bluish discoloration of hands and feet in response to cold.
and last of all it needs to be backed by blood work up which should suggest an autoimmune disorder.