She has set up a website to see if other children have developed the symptoms after taking the drug called Pandemrix.
But the makers claim there is no evidence of any connection and point out that only seven children have developed the syndrome from six million doses of the vaccine in the UK.
The vaccine is manufactured by GlaxoSmithKline, whose UK medical director Dr Pim Kon, said: "There is currently no evidence at all to suggest there is a causal link between Pandemrix and narcolepsy.
"We are working very hard with the regulatory authorities to try to understand what is happening.
"At the end of day, patient safety is of utmost importance to us and we wouldn't ever put out a drug or leave it out there if we believed that it actually was a true issue."
Other tests in the UK have not revealed a link between Pandemrix and narcolepsy, although the Medicines and Healthcare Regulatory Agency said "a similar risk had only been confirmed in Finland and Sweden".
In Finland, investigators found 79 vaccinated children and adolescents had developed narcolepsy, 12 times more than they would expect.
The Finnish government said it accepted a link between Pandemrix and narcolepsy and has promised compensation and support for affected families.
The Finnish Health Minister Paula Risikko said: "We have decided to take these measures because the decision to acquire the vaccine was ours under the threat of a pandemic, and therefore we want to take the responsibility for the outcome."
Josh, from Frome in Somerset, had shown no symptoms of narcolepsy prior to February 2010, and it took another year for doctors to diagnose the condition.
Mrs Hadfield said her son "became a different boy" soon after receiving the vaccination, and Josh was also found to have cataplexy which makes his muscles collapse whenever he laughs.
She said: "Initially, I put it down to being the end of term, coming up to half-term week.
"He was tired and then he started losing muscle control so he couldn't hold things properly.
"We are working very hard with the regulatory authorities to try to understand what is happening.
"He needed you to support his hand because it was just dropping forward. It was horrible."
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