Question

while(getline(INPUT,textLine))
  {
    Object* s = new Object(textLine);
    }

How would I hold a reference to the Object of the previous textLine so that I could compare the two in some compare method

s.Compare(***); <– comparing the second iteration to the first

Note that *** is of type Object

Answer 1

You want to keep track of the previous instance of Object?
Put it in a variable (called t below), and use the variable when you need it.
Remember to delete everything you allocate.

Object* s;
Object* t = NULL;

while(getline(INPUT,textLine))
{
    s = new Object(textLine);
    s->Compare(t);

    delete t; 
    t = s;
}