Desiree Phillips, 20, took the pills to cope with post-surgery pain after she had a number of benign lumps on her breast removed earlier this year.
She had been prescribed anti-biotics and over-the-counter paracetamol but her family suspected she was taking more than the recommended dose before she was admitted to hospital with a failing liver nine days after the operation.
The single mum of a one-year-old son, from Llanelli, South Wales, died at Birmingham Queen Elizabeth hospital on August 26 after enduring a week of excruciating pain and a liver transplant.
"She must have been taking a few extra tablets than the recommended eight a day," her grandfather Des Phillips, 58, told the Daily Mail.
"She seemed fine to us, then out of the blue her boyfriend found her stretched out on the sofa.
"When we heard she was at hospital we never expected she might die. People don't realise that an extra two over a period of time can harm your liver if you keep taking that over two to three weeks."
Although an inquest is yet to be held, Desiree's family want action to try to prevent similar tragedies.
"Cigarettes have a label saying 'smoking kills' but paracetamol packets don't look dangerous," said Mr Phillips.
Desiree's son, Jayden is now being cared for by his father.
A Medicines and Healthcare Products Regulatory Agency spokesman said: "Paracetamol is a safe and effective painkiller when used correctly and when dosage recommendations are followed.
"Every pack has a warning about overdose and instructions not to take more than eight tablets in any 24-hour period."