One year old

My niece is 13 months old and she throws horrible tantrums, it doesn't matter if you are playing in the floor or tell her no that she can't do something.  She will scream and cry and throw herself back and sometimes shake all over and it seems that nothing soothes her. We have tried just letting her throw her tantrum but she is a very head strong child and will not give up. If you pick her up and hold her she still throws a fit, we are kind of in a bind because we don't know what to do or if something is seriously wrong with her.  We thought that she might be sick so we took her to the doctor and they said that she had a little cold but no ear infection and the doctor didn't think that she was teething. What do you suggest to do?