She took a regional flight on 17 March and 10 days later developed symptoms of the respiratory virus.
The woman, who RNZ agreed not to name, said it was nothing like she had ever felt before.
"My lungs started burning, I didn't get the normal flu symptoms, I had that a little bit later on, but it was just my lungs have never been affected in that way.
"The burning then started to become painful with coughing and it felt like a weight on my chest that every day that I had the virus and extra extra weight got put on there, it was just a little bit harder to breathe," she said.
On developing a fever she rang Healthline but was refused testing because she had no contact with a confirmed case and the tracing team had not made contact to suggest otherwise.
"I tried again a second time and told them I'd been on a regional flight with international people and was refused."
She got so sick she contemplated going to the hospital, but instead looked through old media releases and found a flight from the 17 March listed as one which had a confirmed Covid-19 case on it.
The man had flown in from Barcelona before travelling regionally.
She found a story where the district health board's Medical Officer of Health said they would be contacting the close contacts from the international flight.
"I didn't actually pick up at the time, they will only contact trace the international flights.
"And they hadn't even bothered to ring up the regional flight members who he'd been in contact with the same day. And I thought that that was pretty poor."
At this stage it had been over two weeks since she was on the flight and still no contact from the Ministry of Health or tracing teams.
She was able to get tested after proving she was on a flight with a confirmed case.
The results came back negative, but she was told there were lots of false negatives, so she was a probable case of Covid-19.
The woman was asked to go back and get re-tested a week later, but when she did her symptoms were clearing up and she was denied.
During this time she was allowed into a medical centre, despite her protests as she was still showing Covid-19 symptoms.
The staff at the centre said the negative test result meant she could come in.
Four and a half weeks after the regional flight where she came into contact with a man with Covid-19, the Ministry of Health's contact tracing team called her up.
"[They] advised me that I'd been in contact with a Covid sufferer on 17 March.
"This was over a month later and advised me to go and get tested and ring the health line.
"I thought it was a bit late now.
"I rang up the health line dutifully, like I was told to and they said it's too late."
She said the whole situation "reeks of incompetence".
"I must admit, my reaction was to just laugh at the tracing officer, not in a nasty way, but I just laughed.
"I couldn't believe it, that's four-and-a-half weeks later, you've got to be kidding me."
The Ministry of Health said in a statement it was difficult to comment on the specific case.
"What we can say is our case definition for contact tracing people on an aircraft is those sitting within two seats in all directions.
"Other people on the flight would have been considered casual contacts," the statement said.
"We acknowledge that it would have been too late for her to be tested once the contact tracing team contacted her, the passenger would have been able to identify whether any of her close contacts had become unwell and they could have got tested."
