Can I sue the hospital I checked no for my child to have a ssn but they sent my info any ways now my child has a ssn with out my concent

It is unfortunate that the hospital did not heed your wishes, but I'm not sure you have any recourse.  In almost all civil suits, you must show actual monetary damages in order to get relief.  How did the hospital's mistake damage you and/or your child?  Emotional distress or aggravation is not compensable in this situation.