I would say that Della's major conflict is actually of the character vs. character variety. She worries a great deal about what her husband, Jim, will think of her once all her beautiful hair is gone, but she only "faltered for a minute" and lets a few tears fall when she fights with herself about whether or not to actually sell her hair. It does not take her long to make a decision, and, once she does, she acts immediately. However, Della says to herself regarding her husband:
If Jim doesn't kill me [...] before he takes a second look at me, he'll say I look like a Coney Island chorus girl. But what could I do?--oh! what could I do with a dollar and eighty-seven cents?
When Jim does walk in, he has an expression on his face "that she could not read, and it terrified her." She fears that he will not think she is pretty anymore now that her hair is gone. His response, looking around the room with a rather vacant expression and "an air of almost idiocy," makes her really nervous that he is angry with her. This conflict is more imagined than it is real, of course. Jim is only shocked—especially because of his gift to Della—and not angry. However, we do not know that right away, and neither does she.