Get hold of Titanic, Triumph and Tragedy by J P Eaton and C A Haas, this has a chapter called 'Rescue" which has several photos of survivors. I guess they recovered as best they could while mourning their lost loved ones. You could also go to Library, one book I recommend is Titanic Story as told by the survivors by Winocour (someone might be able to help with exact title.) Walter Lord's A Night to remember also has clues
Check out my article: Eric Cimino, "Carpathia's Care of Titanic's Survivors" in Voyage: Journal of the Titanic International Society 101 (2017): 23-31. It describes the activities on the ship as it journeys to New York.