Maybe Snape uses this discovery as an opportunity to teach Hermione something new. He could be curious about how she got the condition on her arm and offer to show her a spell or potion to heal or manage it. This would also be a chance for him to show a different side of himself, not just the strict professor.
She might be initially defensive. Hermione is a proud and independent character. So, when Snape finds out about her arm, she could be worried that he'll use it against her in some way, like taking away house points or using it as an excuse to give her extra work.
One possible reason could be the stress from her studies. Hermione is always under a great deal of pressure to excel academically. Maybe she reached a breaking point due to the overwhelming workload. Another reason might be some kind of conflict with her friends. For example, if she had a big fight with Harry or Ron over something serious, it could leave her feeling broken.
Socially, it could be difficult for him. If others find out that he still has feelings for Lily and she's pregnant, he could face ridicule or be the subject of gossip. Also, depending on his relationship with Lily's partner, there could be conflict. He may have to face the fact that he has to keep his distance more than ever to avoid causing trouble for Lily and her unborn child.
One consequence could be that Hermione has to face the Malfoy family. They might try to bring her into their way of life, which she has always opposed. It would be a struggle for her to keep her own values intact while dealing with their pure - blood traditions.
One possible consequence could be a shift in the power dynamics within the village he leaves. His departure might leave a void that could be filled by either positive or negative forces. Also, his friends would likely be deeply affected, feeling a sense of loss and perhaps even betrayal.
Perhaps she's being bullied. In the wizarding world, there could be other students who pick on her because she's a 'Mudblood'. This could be really distressing for Hermione, and when Snape finds her crying, he might be conflicted between his general dislike for Gryffindors and his sense of justice.
One possible reason could be that she was attacked by some dark creatures while on a solo adventure in the Forbidden Forest. The forest is full of dangers, and Hermione, being brave and curious, might have ventured too deep and got injured by a creature like a werewolf or a giant spider.
Well, Snape is a rather strict and no - nonsense teacher. He might be initially shocked or appalled. He could give Hermione a stern lecture about focusing on proper academic work instead of fanfiction. Maybe he'd even deduct house points if he thought it was a waste of her time or inappropriate.
Well, Harry might feel betrayed. He could be really angry at Hermione and it might strain their friendship. He might demand an explanation right away.
She might get detention. Snape is strict, and cutting class is a serious offense in Hogwarts. He could assign her to clean the potions classroom or help with sorting ingredients in the dungeon.