Snape could be quite startled. He doesn't expect Hermione to come to him for help. In the normal Hogwarts dynamic, they are not on the friendliest of terms. His initial reaction might be a moment of shock, followed by quickly composing himself and putting on his usual cold and aloof facade while waiting for her to explain herself.
He might be initially suspicious. Snape is a complex character. He's used to being on his guard, especially with Gryffindors like Hermione. So, his first reaction could be to wonder what Hermione's real motives are for seeking his help.
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 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.
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 is likely to be initially suspicious. He has long held a rather negative view of Harry, so when he discovers Harry is good at potions, he might think Harry has some ulterior motives or has received improper help. After all, in the regular Hogwarts setting, their relationship is quite tense.
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 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.
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.
In many such fanfictions, Snape might notice Hermione's change in behavior. For example, she could become withdrawn or less enthusiastic in class. He's a very observant character, and her academic performance might also start to decline. He could pick up on the signs during one of his patrols when he sees her looking distressed or if he overhears something that makes him suspect she's 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.
He might immediately go into a protective mode. He could use his potions knowledge to quickly make a healing draught for her. After all, Snape is very skilled in potions, and Hermione being hurt would likely trigger his instinct to help.