Jemma Joslyn, 32, from East Sussex, claims she suffered serious injuries when the woman emerged from a waterslide and crashed into her feet first.
Joslyn’s lawyers said she was taken to hospital with internal bleeding, liver and kidney damage, five broken ribs and fluid on her lung.
Mother-of-two Joslyn had only just arrived at the Liberty Hotel Lykia resort when the incident happened.
The health care assistant said Cook failed to assist her after the incident or ensure her children, aged eight and five, were safe and cared for, despite the family travelling with friends.
Joslyn spent eight nights in hospital in total, including three in intensive care.
She claims there was no lifeguard on duty or traffic light system in place to ensure the slide was safe.
“The woman came hurtling down the slide as I was just standing up to get out,” she said. “I would say she was easily travelling at around 30 miles per hour.
“The impact sent me flying backwards into the water and I instantly started panicking she had come down after my daughter and crushed her at the bottom.”
Magdalena Knez, travel litigation solicitor from Joslyn’s representative Slater and Gordon, said: “My client could have spent her life needing serious medical attention due to the fact the swimming pool slide was not operated with the appropriate safety measures.
“At this point, we are still unclear as to the extent of her injuries and the long-term effect this will have on her health.
“Every British holidaymaker has the right to be protected by their holiday provider, who should provide adequate care while they are abroad. Family resorts should be a safe haven.
“A simple thing such as having a lifeguard on duty could have stopped this incident happening.”
A Thomas Cook spokesperson confirmed the operator had received Joslyn’s claim, adding in a statement: “Both our UK-based welfare team and our in-resort team have been in touch with Ms Joslyn on several occasions following this accident.
“We also arranged for her parents to fly to Turkey to be with their daughter.”
