Nah, there's no indication in Jeongwon's backstory that she lost any part of her memory. She fully remembers her shitty abusive parents and how they died in the same accident, and she was cogent enough during their funeral that people were badmouthing her. (If she'd lost her memory due to a massive head injury, I imagine the gossip in the funeral flashback would have had a very different vibe. At the very least somebody would have mentioned it.)
It also wouldn't make much sense with regards to her phobia. She's afraid of riding in cars, because being inside a car is specifically what triggers her PTSD about the accident, but she had no problems riding a motorcycle with Jisoo.
That isn't typically how amnesia works, contrary to what bad soap operas might want you to believe. And we're suggesting that She lost her memory just of her friends, (Not just Jisoo, but also Jeongwoo,) but then....what? Faked her death? Ghosted Jisoo without ever even seeing her? And then, what? She adopted a new identity for no reason and developed a mysterious phobia of being in cars just...because? And also she completely forgot how to ride a motorcycle, or that she had owned one, and nobody that knew her ever mentioned it. Not one well meaning but annoying relative who was like "Well, you know, this is why we didn't think you should have a motorcycle...."
Sorry, I just don't see any way for this to be even slightly true without some seriously awful writing.

WHAT if Jeongwon is the girl that Jisoo is talking abt and that Jeongwon lost her memory!?!
Cuz Jeongwon got into a car accident but from the drawings it didn't rlly show that she was inside the car, plus the color of the motorcycle that the friend of Jisoo got into had red in it and in the drawing of the car accident u could see a piece of red fragment on the ground! (⊙…⊙ )