First time working with iterating through a linked list. How is my source code so far? Is it safe?

I need to implement a linked list function called:

bool LinkedPolynomial::Add(const double co_item, const int exp_item

It is suppose to:

1) Return false if there is a Node with the same exp_item and do nothing else.

2) Check to see if the linked list is already empty, and if it ISN'T I am to add that node to the list.

3) Check to see if the linked list is empty, and if it IS I am to add the Node the END of the list and return true.

I think I'm close to a correct solution. Here is my work for far:

bool LinkedPolynomial::Add(const double co_item, const int exp_item)
{
  Node* count = head_ptr_;
  while(count != NULL)
  {
    if (count->GetExponent() == exp_item)
    {
      return false;
    }
    count = count->GetNext();
  }

  Node* next_node_ptr = new Node(co_item, exp_item);

  if (head_ptr_ == NULL) // For first addition to the list.
  {
    head_ptr_ = next_node_ptr;          // New node is now first node
  }

  Node* count_2 = head_ptr_;
  while (count_2 != NULL) // For any addition to the list that isn't the first addition. 
  {
    if (count_2->GetNext() == NULL)
    {
      next_node_ptr = new Node(); 
    }
    count_2 = count_2->GetNext();
  }

  item_count_++;
  return true;
}

Are my iterative loops correct? I feel this is a sloppy implementation. I would like to do the second and third steps at the same time, but can't think of a way.