Does NHS cover me while I'm hospitalised overseas?

In my home country (USA)?  I'm a student, so there's no way I can pay for the 10 days of my hospital "visit".

You need to take out travel insurance.  You woul be covered in countries with an agreement, but the US does not have one.

You may be able to get cheap travel insurance to cover you while you're in the US, although a lot of companies do require that you are a UK permanent resident, so you might need to do some digging around for insurance.

I would have a word with your university's international office or maybe a student travel company like STA to see if they know of any insurance policies that you can take out. The UK STA site states that you have to be a UK resident, or resident in the UK for at least 3 months, and starting and ending your journey in the UK. Their 12-day insurance policy starts at £30 .

just from the way your post is worded...are you in the US now (and have just spent 10 days in the hospital?)  If so, then the comments about travel insurance are moot (unless you already have some) as you can only get it before your trip, and you'd be on the hook for all medical costs incurred.    You might be able to work something out with the hospital, though.

But of course if this is a hypothetical question, bookgrl and ksand24 are right on with the insurance recommendation.

just from the way your post is worded...are you in the US now (and have just spent 10 days in the hospital?)  If so, then the comments about travel insurance are moot (unless you already have some) as you can only get it before your trip, and you'd be on the hook for all medical costs incurred.    You might be able to work something out with the hospital, though.

Ah, yes, I might have misread the OP - I read it that you were wanting insurance for a 10-day trip to the US... but if you are in the US now and have been in hospital for 10 days, then no, you are not covered by anything unless you took out travel insurance for the US before you left the UK.