There are many different types of hearing loss and hearing impairments. Damaged Hair-cells (actually it's the stereocilia) are only one type that happens mostly to people who are exposed to high sound pressure over a long time (or very high sound pressure over short time). Constant noise of a city is not nearly loud enough to do that physiologically.
But listening with inear headphones can and will damage your hair cells if you listen too loud regularly.
Regarding hearing tests: Forget online hearing tests - they're total bullshit. Even many of the tests done by professionals result in useless data because it's you who needs to tell them whether or not you hear a specific frequency. And the result only compares your abilities to a standard for your age (see below about individuality). Therefor the results are highly dependent on you're psyche, health, mood,...
Another mixup is sound pressure (physical volume) vs subjective loudness. High sound pressure can damage your hair cells, high loudness cannot if sound pressure is reasonably low. While the thing with loudness wars is bothersome sometimes, it's not dangerous.
Oh I forgot about frequency related hearing loss: Many people think that you can hear 20-20000Hz, but this is only a rough estimation and more importantly highly individual and age related. So it's totally possible that your same-age friend does or does not hear frequencies you do. Most people don't get past 16-17k at all. Secondly, the highest frequencies you're able to perceive get lower and lower as you get older. Many old people can't perceive frequencies higher than 8-10kHz. While they hear worse then others the critical frequency areas for speech (formants) lie way below that. Even music perception works quite fine (although it won't be that crisp anymore).
Tinnitus is another story which can have so many causes (destroyed haircells being only one), stress, tendons in the neck and some others.
So don't pull up the volume unnecessarily on your earphones and you'll be fine.
Edit: Fixed typos.