Hermione would probably be angry at being put in such a situation. She might try to enlist the help of her friends, like Harry and Ron, in a very secretive way. She would be careful not to expose the blackmail completely because she doesn't know how Snape would react if he found out she was trying to get help. She could also use her vast knowledge of magic to create some sort of protection or counter - measure against Snape.
She might initially be shocked and scared. But then she would start to think rationally and try to find a way to outwit Snape. For example, she could start to gather evidence against Snape's own wrongdoings, if there are any, so that she can turn the tables on him.
Hermione usually reacts with a mix of anger and determination. She's not the type to be easily pushed around. So, she might start by trying to figure out who the blackmailer is and what their motives are. For example, she could use her intelligence to set traps or follow leads to expose the blackmailer.
One possible plot could be that Snape discovers Hermione has been sneaking into the restricted section of the library for some research that could get her in big trouble. He threatens to expose her to the school authorities unless she does his bidding, like helping him with some dangerous potions experiments. This would put Hermione in a difficult situation as she doesn't want to break the rules further but also doesn't want to get in trouble.
Hermione may also start to scheme. She'll use her intelligence to come up with a plan. For instance, she might start to collect evidence against Snape, something that she could use to counter his blackmail. She'll research old school rules or find out secrets about Snape that she can hold over his head instead.
Snape might initially be shocked. He's not one to show much emotion openly, but internally he could be very disturbed. He might start investigating what happened to Hermione immediately, using his skills in potions and magic to try and find a cure or at least understand the cause.
Snape would probably be quite surprised at first. Hermione is known for her academic prowess and self - sufficiency. His reaction could range from being dismissive, thinking she should be able to solve her own problems, to being intrigued by the nature of her request. If it's something related to the dark arts or a mystery in the wizarding world, his interest might be piqued, but he'd still be guarded in his response. He might even try to use her request as a way to gain some advantage or information for himself.
Hermione would probably be very confused at first. Snape has always been a rather intimidating and strict teacher, so his sudden change in behavior would be quite a shock. She might initially think it's some sort of trick or test.
He could also be a bit sarcastic in his response. Snape has a sharp tongue, so he might say something like 'Miss Granger, what makes you think I have the time or inclination to help you?' But as Hermione explains her situation, he might gradually soften, realizing the seriousness of the matter. Maybe he starts to see a bit of himself in Hermione's thirst for knowledge.
Snape might be suspicious at first. He might think it's some sort of trick or part of a bigger plot. However, as he observes Hermione more closely and realizes the genuineness of her situation, his attitude could gradually change to one of reluctant assistance. He might even offer some words of wisdom, albeit in his typical sarcastic way, to help Hermione regain her strength.
Snape might initially be taken aback. He's used to students being intimidated by him, so Hermione's outburst could shock him into momentary silence. Then he might retaliate with his usual sarcasm, trying to put her in her place.
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.