The head of the NSW Ambulance service, Dominic Morgan, said some of the emergency calls were taking paramedics' time away from the vulnerable and putting people requiring genuine treatment at risk.
Last night Ambulance NSW had its second ever status three alert, which means the service was unable to meet demand.
"When we receive calls that do not require an ambulance immediately, it can have dire consequences," he said.
"I have been advised this week that we had a 25 minute response to an 18-year-old cardiac arrest. This is devastating. Wherever possible we need to be avoiding this."
Last night alone, NSW Ambulance received 2500 calls from coronavirus patients under lockdown.
Some calls from residents included being asked for a lift to vaccination clinics.
Dr Morgan said the past three days have been exhausting for the service, with 450 calls yesterday.
"Over the last three days, New South Wales ambulance has experienced call demand equivalent to our busiest New Year's Eve," Dr Morgan said.
"These are extraordinary times and it places great pressure on our staff when we receive some calls that may not be medical emergencies.
"Our triple-zero call operators have received calls to help take food to people's houses, triple-zero cannot help you with this. We have received calls for people to be driven to vaccination centres, triple-zero cannot help you with this."