I don't think so.
After Harry learns what the third task will consist of (getting
through a maze) and then runs into Barty Crouch Sr and all that jazz,
the trio get in training.
For the next few days he spent all his free time either in the
library with Hermione and Ron, looking up hexes, or else in empty
classrooms, which they sneaked into to practise. Harry was
concentrating on the Stunning spell, which he had never used before.
'Well, I think Harry's got it now, anyway,' said Hermione
hastily. 'And we don't have to worry about Disarming, because he's
been able to do that for ages ... I think we ought to start some of
these hexes this evening.'
She looked down the list they had made in the library.
'I like the look of this one,' she said, 'this Impediment
Jinx. Should slow down anything that's trying to attack you,
Harry. Let's start with that one.'
Harry Potter and the Goblet of Fire - pp.498-9 - Bloomsbury - Chapter
29, The Dream
So, much like with the second task, they've been trawling through
library books, compiling a list of useful-looking spells and then
Harry then has his dream where he sees Wormtail getting tortured and
goes to tell Dumbledore. He then takes a trip down memory lane through
After this, they set to it again, and that's where we get the quote I
mentioned above. Note that the Impediment Jinx (one of the spells on
their list) is explicitly mentioned. What follows this quote is a bit
about Harry's troubles with the Shield Charm and then:
'You're still doing really well, though,' Hermione said
encouragingly, looking down her list, and crossing off those spells
they had already learnt. 'Some of these are bound to come in handy.'
Harry Potter and the Goblet of Fire - p.529 - Bloomsbury - Chapter
31, The Third Task
In this context, it really sounds to me like Hermione "discovered" the
spell in a book, that is:
- Find unexpectedly or during a search:
'firemen discovered a body in the debris'
I would argue she dug it up and added it to their list, rather than
that she invented it.
In addition to this, I consider Hermione someone who takes a very
by-the-book approach to her magical education, e.g. (one example of
very, very many):
'Mandrake, or Madragora, is a powerful restorative,' said Hermione,
sounding as usual as though she had swallowed the textbook.
Harry Potter and the Chamber of Secrets - p.72 - Bloomsbury - Chapter
6, Gilderoy Lockhart
I don't really think she's the sort of person to experiment with her
magic, and at this desparate time, when the Third Task is imminent, I
can't really see her messing about with her own creations.
Also, as I mentioned under the linked question, she seems - at the
very least - cautious about non-approved spells:
'So you just decided to try out an unknown, handwritten incantation
and see what would happen?'
'Why does it matter if it's handwritten?' said Harry, preferring not
to answer the rest of the question.
'Because it's probably not Ministry of Magic-approved,' said Hermione. 'And also,' she added, as Harry and Ron rolled their eyes, 'because I'm starting to think this Prince character was a bit dodgy.'
Harry Potter and the Half-Blood Prince - p.226 - Bloomsbury - Chapter 12, Silver and Opals
There is a much larger dimension to this - her mistrust of the Half-Blood Prince and her mistrust of other people's incantations, scribbled down in a book, which could be anything. Of course this mistrust may not apply to her own spells, but, still, I can't personally see her inventing spells, to be honest.
Anyway, that point is arguable, but I would also say surely, surely, if 15-year-old Hermione had invented the spell herself, Jo Rowling would not have left it so unclear, nor remarked upon it so tangentially. From an out-of-universe perspective, I think JKR would have made a much bigger deal out of it, if she'd intended to say that it was Hermione's own creation. For me, the very ambiguity is reason enough to believe "discovery" here means something she found, in the books that they'd been searching through in the library, which was, of course, the well-established context of this remark.
Finally, I would point to the fact that it has a name - the Four-Point Spell - that is different to its incantation (Point Me). This is, surely, not proof positive, but where did the official-sounding name come from? For sure, Hermione could have invented it and named it, but to me, it really sounds like "the Four-Point Spell" is the name the spell appears under in a textbook, with its associated incantation given underneath.