Yes I'm sensitive to some sounds. Continuous sounds usually aren't very intrusive while intermittent ones often are, but I guess that's normal. Strongly dislike rap music but that's probably because it usually comes from cars and for some reason it's usually very loud and bassy, and I've no control over whether or not I can hear it.
When I'm trying to focus on something I find difficult to focus on, like a problem that challenges my mind strongly, the slightest noise usually shatters my concentration, though if I can drown the noise out by playing continuous pink noise or rain and thunder effects, I can continue OK. Sometimes I really push my brain to its limits and I know that if I stop focussing, my poor short-term memory will have a lot of trouble getting back to where I was, so even fairly quiet intrusive noise can be a big issue if I feel that what I'm trying to think through is of any great importance. It's like trying to count up a large number of items and then somebody bursts a paper bag and I have to start all over again.
I'm also rather sensitive to harshness in sound recordings, such as distortion in old vinyl records, especially if there's an orchestra. It completely ruins the experience.