Sarah Williment's son, Jack, was rushed to the Leeds hospital by ambulance with suspected pneumonia on December 3.
However, during the busiest week the A&E had seen since 2016, Sarah, 34, said her son was left in a clinical treatment room for over four hours.
A photograph sent to the Yorkshire Evening Post by Sarah shows Jack with an oxygen mask, lying on a pile of coats for comfort on the floor of the room.
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The boss of Leeds Teaching Hospitals NHS Trust, which runs the A&E department, personally apologised to Jack's mum.
Sarah, a primary school learning mentor, said the hospital staff were "all as helpful as they could be" but "there simply aren't enough beds to cope with the high level of demand".
She explained: "The NHS is in crisis.
"We went in an ambulance from our GP as the doctor suspected he was suffering from pneumonia.
"We bypassed A&E on the way in but it was so busy.
"There are just not enough beds."
Jack was originally placed on a bed in the Paediatric Emergency Department.
However - due to an emergency arrival at the hospital - Jack was told that the bed was needed for the other patient and he was moved into a clinical room, his mum said.
Sarah added: "A doctor rushed in and said he needed the bed.
"We were taken out of that room and placed in another room which had no bed to lie in.
"My son was forced to sleep on the floor.
"He just couldn't settle or get comfy, he said he wanted to lay down.
"He was not able to settle, he kept sitting on the floor.
"Jack's coat was on the floor and he ended up laying on top of it."
Jack - who was using an oxygen mask while laid on the floor - was diagnosed with Influenza A and Tonsillitis by doctors.
He left the hospital shortly after lunchtime on December 4.
Sarah added: "He spent eight and a half hours in A&E, more than twice the required waiting time which is normally four hours.
"Jack wasn't provided with a bed on a ward until 13 and a half hours later."
Sarah said the NHS is in crisis and said the system was to blame for the lack of beds.
She said the LGI staff were very helpful but was dismayed at the fact her son had to spend so long without a bed.
Dr Yvette Oade, Chief Medical Officer at Leeds Teaching Hospitals NHS Trust said: “Our hospitals are extremely busy at the moment and we are very sorry that Jack’s family had a long wait in our Emergency Department. Our Chief Executive Julian Hartley has spoken to Jack’s mum and offered a personal apology.
“We have seen a significant increase in the number of people visiting our Paediatric Emergency Department, and this week we saw the highest attendances we have seen since April 2016. Despite this, our staff are working tirelessly to provide the best possible care under these extreme pressures.
“Jack was quickly assessed upon arrival and seen in two different clinical treatment rooms in the Paediatric Emergency Department.
“Within four hours a decision was made to admit Jack to our Children’s Assessment and Treatment (CAT) Unit for further monitoring overnight. Unfortunately, the unit was also experiencing exceptionally high levels of demand which meant that Jack was required to wait in the clinical treatment room in the Paediatric Emergency Department until a bed became available. Jack was admitted to the CAT Unit later that evening and was discharged home the following morning after a medical review.
“We are extremely sorry that there were only chairs available in the treatment room, and no bed. This falls below our usual high standards, and for this we would like to sincerely apologise to Jack and his family.
“We are increasing the bed availability in our Children’s Hospital and our Children’s Assessment and Treatment Unit will be relocating to a larger area in the new year. We are continuing to develop the plans for our new Children’s Hospital in Leeds which will be built in 2025.”