Daveanah Cowie, 21, said she was stunned when her pleas for help were allegedly ignored as she cradled the newborn in her arms.
But she ran to find a doctor who resuscitated little Tommy-Lee and put him on a life-support machine.
She says her baby could have died if she had not acted quickly.
Daveanah said that Tommy-Lee was found to have bronchitis and has since been in hospital for more than a week with his twin brother Arlow-Jack, who has the same condition.
She branded staff who saw her on arrival at Derby Royal Hospital as “irresponsible”.
The mother of five, from Alvaston, Derby, said they should be given more training.
She said: “I took Tommy-Lee to hospital because he was poorly and I noticed as I got out of my vehicle that he was not breathing.
“I rushed him through the doors in a panic and asked the receptionist to get help immediately.
“Instead she decided to take my details and told me to sit down and wait my turn. I couldn’t believe it. My baby was not breathing and I was told to wait. I ignored that and found a female doctor. If I had waited my baby could have died. After I found the doctor, Tommy-Lee was ventilated and transferred to Queen’s Medical Centre in Nottingham.”
The drama took place when Daveanah rushed the babies to Derby’s main hospital on November 27.
Last night Tommy Lee was still on a ventilator but he and his brother were slowly making a full recovery.
A Derby Teaching Hospitals spokeswoman said: “Our priority is always the safe care of babies and children brought to our children’s emergency department. Thanks to the expertise of our emergency team, the baby in this case had appropriate care.
“We were concerned to find that a receptionist failed to recognise the serious nature of this situation as this is highly unusual for our dedicated team of reception staff.
“We immediately started an investigation and we are now reviewing the training we give to reception staff in the children’s emergency department.”