Thankfully doctors were able to remove the tumour and a year later Cocchiara was told she was in remission.
Cocchiara said: "I couldn't believe it at first, I was so sure that I was pregnant again and never in a million years did I think it would turn out to be cancer.
"My symptoms mimicked my first pregnancy, I had missed a period, my breasts were tender, I was irritable and hungry all the time.
"The pregnancy test even confirmed I was pregnant and so I didn't have reason to believe otherwise.
"But my hormone levels were sky high which later alerted doctors to the cancer.
"After being diagnosed I was terrified, I couldn't imagine being without my daughter and I knew I needed to get better for her.
"A week before they told me it was cancer I had a tumour the size of a grape fruit removed from just outside of my uterus.
"Doctors are unsure of how it happened but somehow cells from my placenta broke away and escaped out of my uterus, they also had to remove my right fallopian tube.
"With Madison I had a natural labour that seemed to be completely normal, nothing went wrong and there were no signs that anything unusual had happened.
"But even now, knowing that having Madison triggered the cancer I wouldn't change a thing, I don't regret having my daughter and never will.
"I wouldn't change her for the world and I would do it all over again given the choice."
Although choriocarcinoma can happen after any type of pregnancy, it is very rare and only occurs in around one in every 50,000 pregnancies.
Thankfully Cocchiara's cancer was caught just in time, but doctors warned that if her tumour hadn't been removed when it had then the disease could have spread to her lungs.
She added: "After taking the pregnancy test I went to a clinic to get checked out, nothing was found on the ultra sound which I assumed meant I was really early or I had an ectopic pregnancy.
"But after further tests, I was diagnosed with cancer and needed six lots of chemo over a 12 week period, I lost my hair but surprisingly that didn't bother me as much as I thought it would.
"I actually felt quite free, it made me realise that there is other things in life that make you look and feel beautiful and my daughter was a huge part of that.
"During the last week of my chemo I had a concentrated amount every day and then my bloods were taken and monitored every month for the rest of the year."
In May 2015, Cocchiara was given the news that she was in remission, and has since been rebuilding her life.
She said: "It may still be possible for me to have more children in the future, despite my chances being a lot lower, but for now I want to make the most of every day I have with Madison.
"I know I would spend every minute wondering if I was going to get cancer again, and I'm not prepared to live my life like that.
"It was also a particularly hard time because I had no health insurance so my friends held a benefit for me and raised over $10,000 to help with our rent and bills as I could no longer work.
"Even though I was given the all clear the treatment left me with some lasting effects, I often forget things and I try to make lists to help me remember.
"I also gained 25lbs from being on steroids, I have struggled with my weight but I am finally getting on the right track now."