If I understand your question, I assume you are asking about the symbolism of the snake in the short story "Sweat."
The story is about Delia, the wife of an abusive husband. She has worked hard to put food on the table and to buy her house, and her house is the most important thing in her life. She is respected by other men in the community who watch her work each day and watch how her husband treats her. They have no respect for him, and feel badly for her for they find her an admirable person.
Her husband (Sykes), on the other hand, is not only physically and verbally abusive, but he is openly having an affair with an uppity, brazen woman. Even in light of the anger and shame the presence of this woman brings her within her community, Delia continues to bring in the laundry of white folks to support them, even while Sykes verbally abuses her for doing so.
Amid all this, the only thing that Delia cannot abide is a snake of any kind: she is deathly afraid of them.
At the start of the story, Sykes enters their home flicking his whip so that it lands like a snake on her shoulder. This not only gives an indication of her passionate fear of them, but provides foreshadowing as to the story's conclusion: it is a snake Sykes unleashes in the house to kill Delia that, in fact, bites and kills Sykes instead.
Perhaps because of its part in the story of the Garden of Eden, the snake is symbolic of temptation and/or evil. In this story, the snake is certainly symbolic of evil: of Sykes' evil.
It might also be perceived as being symbolic of Sykes's physical power over Delia. He is a large man, while she is thin and slight (something about her that he hates).
It may represent his sheer sexual aggression and Delia's frailty as a woman. However, there is no longer a physical relationship between the two during the course of the story. She works to support him and has paid for the house, and he keeps another woman on the side, beating Delia whenever he feels like it.
In terms of the snake being a phallic symbol, when it arrives it is full from eating frogs and slow to move. When it returns to its senses, it is energetic, quick and deadly. It is phallic in this sense.
According to eNotes "Sweat/Themes," the phallic symbolism of the snake is a prominent part of the overall sex theme in "Sweat." The phallic symbolism begins with "something long, round, limp and black" that falls on Delia’s shoulders. This reference is so constructed to shock the reader into paying attention to the sex themes (eNotes) that snake their way throughout "Sweat." In addition, Huston links the phallic symbolism with a commentary on Sykes personality (eNotes), which can be seen to generalize on a social cultural level.