Is this The Heroine of Drayfox...?
Hansol is excited to begin her college career when a fatal accident whisks her away to a mystical land. Now in the body of Finea Macaira, the daughter of Drayfox nobility and a descendant of one of the five heroes of the empire, she must learn to forget about the past and embrace this magical new world. It won’t come easy, as Finea discovers within herself a great magical ability that’s powerful beyond her control. Meanwhile, an ancient and destructive force of evil is about to return... But under the protection of the six elemental spirits and a friendly dragon, she may just be able to hone her potential and fulfill her destiny as one of the empire’s great heroes. Based on the hit novel.
In the first chapter, a young Korean woman is fatally injured when another woman shoves her to the ground during an altercation on a train platform, and she cracks open the back of her skull.
In chapter 4, she wakes up in another world as Finea, the newborn daughter of Marquis Caleb McKaira and his wife, Monia, who're portrayed as loving parents. Finea has brown hair, like her mother, and a brother named Felix, who has blond hair like his father, and is three years older than Finea.
One chapter earlier, Finea was lying in her crib in her parents' bedroom when she was visited by half a dozen elemental spirits, who mostly look like glowing adult humans. They gathered around her crib and conversed for some time.
In chapter 10, there's a time skip, and Finea is now four years old.
In chapter 12, Monia takes Finea and Felix out to visit their maternal uncle, Count Douglas Parcy.
In chapter 15, Caleb takes Finea and Felix to the Imperial Palace. In chapter 16, they meet Prince Ophinio Draforcuth, who's the same age as Finea. And in chapter 17, Finea and Ophinio get into a scuffle with one another at the palace's training ground.
I've seen three different covers for this manhwa, but one below bears the closest resemblance to your description.