I would recommend learning more, yes. I know people who practice a couple of different types of magic, and I've at least read up on everything I've ever heard of. Rowling is using what we call the "purely imaginative" school of witchcraft, in which things are possible when they are suitable to a storyline, and words have power if they are sort of a bit of a pun if you know Latin, or just sound cool.
This school of witchcraft is noted for its total and utter lack of interest in any kind of actual functioning magic, and the light-hearted total irrelevance of its study to any kind of formalized magic system.
In other words, IT IS PURE FICTION. It's not the slightest bit similar to any school of magic practiced in the real world. Rowling shows no signs of any clue about real magic, except in that she has carefully avoided anything that might be taken seriously, such as tarot cards. The one crystal ball in the story is portrayed as a device used by sham artists.
There are a lot of false claims made about these books. It's dimly possible that there's a real connection to some kind of magic, but I've read the books a couple times and found no hint of it.
It is certainly not the case that Rowling is applying any knowledge of "real" magic in these books, unless it's by conspicuously avoiding the trappings of traditional real magic. The only thing I've seen in common is that she uses "wands", but her model of what a wand does is totally unlike anything I've seen outside of children's books.
Curiously, she's writing children's books. Maybe that's why she's using the accepted norms of the fantasy genre as much as possible.