The Royal College of Paediatrics (RCPCH) said children’s hospitals, which are usually protected when pressure shows elsewhere in the NHS, are now also feeling the strain of “overwhelming” demand and staff shortages.
Waiting times at A&E have lengthened, and some non-urgent operations have been put on hold.
It comes as rates of non-Covid viruses have rocketed in Scotland.
There were six cases of Respiratory syncytial virus (RSV) recorded per 100,000 people in the first week of October, around six times the rate in the same period in 2020 and 2019. Children under five were the group most affected.
Rates have reduced slightly since then, along with a slight improvement in A&E waiting times.
But the RCPCH warned the situation is expected to get worse over winter.
Paediatric A&E departments are usually among the only areas where the Scottish Government target of 95 per cent of patients being seen within four hours is hit, with most seeing 98 to 99 per cent of patients in this time.
But in the last four weeks, no paediatric A&E department in Scotland has hit the target.
Health boards said the Royal Hospital for Children and Young People (RHCYP) in Edinburgh, the Royal Hospital for Children (RHC) in Glasgow, and the Royal Aberdeen Children’s Hospital (RACH) were all seeing higher than usual demand.
The Tayside Children’s Hospital (TCH), which does not have an A&E department, is also under pressure, and has seen an increase in cases of RSV.
Mairi Stark, Scotland Officer for RCPCH and a consultant paediatrician at the RHCYP in Edinburgh, said the situation is “relative”, and while adult A&E departments often miss targets, it is not usual in paediatrics.
“I've never really heard of breaches at the Sick Kids… and then there was a period of time in September when we were having 20 to 30 breaches a day,” she said.
“It’s all relative, 20 breaches for us is massive.”
She added that the number of admissions has also increased, as some children are “really quite sick” with RSV.
“We’ve had twice as many patients in September than we've seen in a long time,” she said.
“The numbers of admissions are massive, about a 50 per cent increase from what you'd expect at this time of year, and numbers of patients coming through A&E almost double at times what you'd expect at this time of year.
“Usually about 100 to 150 patients come through A&E in 24 hours, and we're having 200 to 250, record numbers of patients.”
While it is usually babies who arrive with RSV, this year toddlers are also being admitted as they may not have built up their immune system during last year’s lockdowns.
Flu has not yet become a problem, but is expected on the horizon, and Dr Stark urged parents to make sure their children get a flu vaccine.
Dr Edward Doyle, Associate Medical Director of Children’s Services at NHS Lothian, said he also expects demand to rise.
"Across our paediatric A&E services, we are seeing greater numbers of children and young people requiring treatment, and we anticipate presentations will continue to rise over the winter months,” he said.
"Despite this challenge, we remain committed to meeting the Scottish Government performance targets on waiting times in our paediatric Emergency Departments and on most occasions, we do deliver to that standard.”
NHS Grampian said patients are waiting “longer than expected” at A&E at the RACH.
“RACH, like the rest of NHS Scotland, is continuing to face unprecedented pressure and strain amid the ongoing Covid-19 pandemic,” a spokesperson said.
“Higher than usual rates for other conditions, including respiratory syncytial virus (RSV), are adding to this.
“These increased pressures - including those on capacity, staffing and increased infection, prevention and control - mean we cannot treat as many patients at one time with RACH A&E as we could previously.”
NHS Greater Glasgow and Clyde has also seen a “significant demand on services” at the RHC, with increases in A&E visits and in paediatric intensive care.
"There have been a few occasions when patients have experienced higher-than-usual Emergency Department waiting times in the hospital,” a spokesperson said.
"This has normally been when an exceptionally large numbers of patients present in a very short period of time. We would like to apologise for any distress experienced during these times.”
NHSGGC said it has also postponed some non-urgent procedures for children, while prioritising emergency, trauma, cardiac, neurosurgery and cancer care.
Some elective care has also been delayed at the children’s hospitals in Edinburgh, Aberdeen and Dundee.
Dr Stark highlighted the impact a surgery delay can have on a child’s life.
“Then there are backlogs, and we're not used to backlogs in paediatrics,” she said.
"We're not used to lots of waiting times, and that makes us more anxious than in adults.
“With children it's more about their lifetimes.
“If you have a child and they've got to wait for elective surgery, say for hernia repair or something like that, then they may have to wait six or eight months.
“But if they're two years old then that's a long time.”
A spokesperson said the the Scottish Government is working to prioritise resources.
“We have worked closely with Public Health Scotland and Health Boards to plan for non-Covid respiratory viruses such as RSV and parainfluenza to prepare for the increases we are now seeing,” they said.
Dr Stark said staff are feeling “overwhelmed”, especially ahead of winter.
Patient safety is the “number one” thing the college is currently concerned about.
But Dr Stark added added parents should still bring their child to A&E if they are worried, and that Scotland’s children’s hospitals are “a safe place to bring your child”.