I assume a few things from Swain's line when he collects a soul fragment from her: "Faces fading in the flames...it was all her fault." I've seen someone else who has the same theory as me: that her parents died in an explosion or a fire, she blames herself for it, and developed a massive complex due to that tragedy. There seem to be hints that Warwick and/or Singed was involved as well. Vi abandoning Zaun for Piltover might have been the last straw though, since the Wedding Crasher reveals that, deep down, she hates upper-class Piltovans for not understanding the hardships of the impoverished people of Zaun.
Assuming this, it does debunk the theory that Vi is her blood-related sister. They don't look too much alike, but Vi is explicitly stated to be an assumed orphan, or at least abandoned as a baby (I have a whole other theory about who Vi's parents are). However, Jinx and Vi were probably in the same Zaunite gang, and Vi might have even been her adopted sister. She and Vi were definitely close originally, which would explain why Jinx is so pissed at her for abandoning both her and Zaun.
Personally, I think her eyes might be naturally red. Akali has reddish-magenta eyes, and she's a human too. There are a bunch of other humans with more unusual eye colors as well, so it might just be a Runterran human thing. As for her original hair color, I'm almost certain it's red or orange-red, especially due to her Odyssey skin. A large majority of her skins portray her with red or orange-red hair (Mafia, Slayer, Star Guardian, and now Odyssey). Even Firecracker Jinx has red braids. Also, her default look has red eyebrows. Since she doesn't seem to bother dying those blue, I think that Jinx is definitely a crazy redhead.