The 15-year-old's loved ones have started a GoFundMe for her, and they've revealed her name as Kaylee ... with them noting that she's battling for her life as she remains hospitalized in critical condition following last week's incident.

According to the GFM -- which is aiming to raise $120,000 to help cover her mounting medical costs -- the brawl left Kaylee with major brain bleeding and swelling.

They also say she suffered a skull fracture and frontal lobe damage as well -- noting she's just at the start of what they consider to be an uphill battle of recovery.

Her family doesn't explicitly say it ... but it sounds like she might not be conscious.

Remember, Kaylee was seen alone and convulsing on the ground as the scuffle continued to play out around her -- which included several other teens throwing punches at one another. According to her family ... EMTs eventually arrived on the scene and rushed Kaylee to a local hospital in St. Louis, but it seems like the damage might've already been done by then.

As we reported ... the teen girl who assaulted Kaylee was arrested on a first-degree felony charge -- but the case is currently being handled by the juvenile court system due to the perpetrator's age.

However, we've learned she could be tried as an adult ... depending on how a court hearing plays out in a couple weeks. If Kaylee's condition worsens, it could spell bad news for the culprit in question too.