The young reality star (whose real name is Alana Thompson), along with her Mama June, and fellow Here Comes Honey Boo Boo family members Pumpkin, Jessica and Sugar Bear were all in the family's 2012 Suburban when the incident occurred.
"It happened so quick," Mama June told PEOPLE on Tuesday. "Before I could say watch out – boom – he had already hit us."
The family was taken to the hospital by ambulance after a 19-year-old boy allegedly driving a vehicle without his lights on crashed into them while speeding.
"Pumpkin went into a full panic attack and has severe bruising on her chest from the seat belt," June, who suffered whiplash plus a back and a neck sprain, explained. "Alana hit her head on the glass."
Sugar Bear, who was driving the vehicle, has a back sprain.
"This is the first wreck that we have ever had, but everybody is doing okay," June said. "Today is Pumpkin's 14th birthday, so we are still going to celebrate."
TMZ was the first to report the incident.
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Reporting by EMILY STROHM