Professor Snape might also be involved. Despite his usual strictness with Hermione, he is a potions master. He could see this as an opportunity to teach her a lesson about being more careful, but also help her because he wouldn't want a student to be in real danger from a botched potion. And there's always the possibility that Dumbledore, with his vast wisdom and knowledge of magic, could offer some cryptic advice that ultimately helps Hermione solve the problem caused by the accident.
Another character who could help is Luna Lovegood. Luna has a unique perspective on magic and often knows about strange and unusual magical creatures and phenomena. She might be able to suggest an ingredient or a method that Hermione hadn't thought of, something that comes from the more esoteric parts of magic that Luna is so familiar with.
One possible plot could be that during a potions class, Draco and Hermione accidentally mix the wrong ingredients. This could lead to a magical reaction that causes them to swap personalities. Hermione might start acting like Draco, being more aloof and sarcastic, while Draco could become more studious and rule - abiding like Hermione. They then have to figure out how to reverse the effect while also dealing with the chaos it causes in Hogwarts.
In a fanfiction about Hermione's potions accident, perhaps she was trying to create a new potion for a school project. But she misread a step in an old, dusty potions book. As a result, the potion explodes and creates a time - warp effect in the potions classroom. Now Hermione has to deal with different versions of her friends from different time periods all while trying to fix the potion to set things right.
It could improve their relationship. After the accident, they might realize that they have more in common than they thought. For example, they both are very determined when it comes to potions, just in different ways. This newfound understanding could lead to a grudging respect and the start of a friendship.
One popular one might be 'The Unforeseen Consequences' where the potions accident leads to them having to work together closely to reverse the effects. It has a great plot that delves into their characters.
Often, it creates a situation where they have to rely on each other. For example, in some fanfics, the accident might give them shared magical symptoms that only they can understand and solve together.
One possible scenario in such a fanfiction could be that during a potions class, Harry and Draco are forced to be partners. They are making a complex potion, and due to their mutual dislike and lack of proper communication, they mess up the ingredients. The potion explodes, covering them both in a strange goo. This accident could be the start of them seeing each other in a different light, perhaps realizing that they are not so different when it comes to making mistakes.
I really like 'The Unforeseen Consequences of Snape's Potions Mishap'. In this fanfiction, Snape's accident in the potions lab creates a magical cloud that spreads throughout Hogwarts. It starts to make everyone act out of character. For example, the Gryffindors become overly studious and the Slytherins start being overly friendly. It's a really fun take on how a potions accident can have widespread and unexpected effects on the Hogwarts community.
Maybe she's having a bad day. Everyone has off days, and Hermione is no exception. She could have had a fight with her friends earlier, or received a bad grade on a previous assignment, and that negative emotion spills over into Potions class.
A great plot point could be that the potions accident results in them being able to read each other's minds. They suddenly have access to each other's deepest thoughts and secrets. This makes them extremely uncomfortable at first, but as they start to understand each other better, they form an unlikely bond. For example, Harry discovers that Draco is under a lot of pressure from his family, and Draco realizes that Harry has his own insecurities despite being the 'Chosen One'.
One idea could be that during a potions class, Harry accidentally mixes the wrong ingredients and creates a potion that makes everyone's voices switch bodies. So Hermione might sound like Ron and vice versa. It would lead to a lot of comical situations as they try to reverse the effect.