Can my family receive compensation along with my slip and fall lawsuit

This sounds like a serious slip and fall.  And, it sounds that you have a number of injuries from this fall.  What helps your lawsuit is that the sidewalk was unattended for two days.  A few hours would be enough, but 2 days helps your case. With regards to your family, how were they injured?   If they were with you when you fell and saw your being injuried, there might be claim for negligent infliction of emotional distress.  In order to qualify for such a claim, your family must have been at the scene of the accident and must be aware that you suffered from the injuries.  Your family must be able to show emotional distress beyond that likely to be suffered by an unrelated bystander who sees the accident.   If they were not with you at the time of the fall, their case for emotional distress would fail.