It started with a spider. Someone with a taste for narrative justice might call it retribution, but there's really no moral correlation between the wisdom of absconding with a relative stranger after a party and waking up the next morning in Brooklyn with a rash of poisonous bites on your arm. When the angels of sexual continence want to punish you, they send crabs not spiders.

I assumed, at first, that the maddeningly itchy marks were the work of common-or-flophouse New York bedbugs, but 12 hours later, with my right arm swollen to the width and purplish colour of a prize turnip, my friend identified the hallmarks of the brown recluse spider, and uttered words I had hoped never to hear on this side of the Atlantic: "You should really get that checked out by a doctor."

I first came to New York to write about the emerging social justice movements associated with Occupy Wall Street. Through my conversations with the protesters in Zucotti Park, I began to understand how profoundly the stranglehold of American private healthcare keeps ordinary people cowed and compliant in the land of the notionally free.

It's not just the 59 million Americans living without health insurance and unable to access treatment for everyday maladies without crippling expense. It's the millions more who dare not risk a dispute with their boss for fear of losing their medical cover, who expect to remortgage their homes in old age to meet the costs of failing health, or who live in fear of bankruptcy should they develop a chronic condition or have an accident.

The notion of a society that sanctions companies to profit from sickness feels barbaric enough, without then forcing ordinary people to choose between medical treatment and the financial future of their families. President Obama's attempt to reform the system in 2009 roundly failed to remove healthcare as a source of perennial anxiety for most American citizens, or to lighten the dead hand of the market on medical provision in the US.

Socialised healthcare is in my blood but, unfortunately last Wednesday, so was a hefty dose of spider venom and several billion extra bacteria – the unfriendly sort that make an infected limb sweat and swell like a rotten root vegetable. I had travel insurance, but no idea if it stretched to the snacking habits of urban arachnids. So I uttered the words familiar to any uninsured or precariously insured American: "I'll just wait for a little bit and see if it gets better."

Had I waited another 24 hours, I might have lost my arm. By the time I was persuaded to go to the emergency response unit at Beth Israel hospital I could no longer move the limb, which was developing worrying purple track-marks. The triage nurse sent me straight through to ER, where I was given a bunk next to a groaning man in his mid-30s who, like me, had been so worried about the cost of treatment that he had allowed an infection to spread, in this case from a rotten tooth. He was already missing several teeth. He told me he was a postal worker with no health insurance, and that he wouldn't have come for treatment had his girlfriend not driven him to hospital when he collapsed with a fever.

Compared to the accident and emergency unit at my local London hospital, the waiting period was civilised; it was a mere hour before a stern-looking registrar arrived to take my money. He explained the covering clauses of my travel insurance and showed me where to sign on several complicated forms. When I explained I was unable to do so because my arm wasn't working, he gave me a look that suggested I'd have had to find a way to sign even if I'd come in with all four limbs off. I signed with my left hand.

After that, the service was exceptional. I was whisked off to intensive care for intravenous antibiotics. I was put in a quiet bed near a window, with no cracks or mildew in the walls, and brought cool water and a clean towel. And when, in the middle of the night, I went into near-fatal anaphylactic shock, the staff's reaction was swift and efficient. I felt, in other words like a valued customer. But it also meant that, at 2am and thousands of miles from home, I was already wondering how I would afford the prescription for all the antibiotics I needed.

This is the difference that social medicine makes to the fabric and quality of life in a civilised country. When I finally wobbled out of the shiny lobby of the Beth Israel, clutching a bag of drugs, follow-up advice and complimentary hospital toiletries, I understood what it really means to be without means in America. Those who are wealthy enough to afford decent healthcare have their needs met in relative luxury, while those who are poor live in fear of getting ill, worrying that one misadventure might leave you with yet more debts to pay off.

No amount of fresh towels and edible breakfasts can make up for the feeling that your health is less important than the capacity of your chequebook. Which is why children and pensioners are still standing in Manhattan's financial district with placards telling the world they cannot afford healthcare, as police patrol the perimeter. And why, when I got out of hospital, I went straight back down to Liberty Plaza to stand with them.