I want to download and install an app on my iPhone, that is available in the US iTunes App Store - but not in my country's iTunes App Store.
Is that possible without creating a US iTunes account or jailbreaking my phone?
It IS possible. I have done this. I can't imagine why an app developer wouldn't want everyone to buy their app.
This whole situation seems to be born out of some aspect of international distribution rights, it's archaic but can be legitimately navigated.
The way you have to do it is to change your iTunes billing information to use an account that is billed in a country where that app is "available". Then you'll be able to buy that content just fine and your existing content will function fine too. I operated this way for about a year. I had a friend open a bank account and I gave him money through paypal. He then let me use that account for iTunes access. I don't know of an easier way....
There are OTHER ways too, but I'm pretty sure such discourse is not permitted here. And actually, I haven't explored those as I fear big brother will have a temper tantrum.
Have you tried going to iTunes on a computer and just changing the store to the US App store? It's a long shot, but there is functionality to shop another countries store simply by clicking the flag at the bottom of your main iTunes store page. Scroll to the bottom and try switching to US.
If you wanted to switch permanently, see here for a self service solution:
I live in Canada and use an alternate account for US only apps. My alternate account just has a fake address/zip code from the US, and as such, is tied to the US App Store instead of Canada's
However, when updating apps it's necessary to enter passwords for both accounts, since both accounts might have apps to be updated.