Normally a list uses two classes: one for the list itself and one for a node within the list. You're using one class to represent both, which is a little unusual.
is also relevant in your case. you should streamline your design and there are several examples on this forum about inserting/deleting nodes based on such design: for eg. this http://www.cplusplus.com/forum/beginner/208086/#msg981383
I'm sure you'll find many more online as well