Courtesy of someone on Yahoo! Answers, I've finally found the song. Thing is, the person answered my question nine months ago, and I've only just now seen it! The song is indeed called “Swim,” by a band called Papa's Culture. My memory of it was only off in regards to there being an aquatic effect to the voice. Not sure why I remembered it that way – maybe because it's about swimming, and I was stationed in Hawaii at the time, or I had wet myself, I don't know. Anyway, here it is, if anyone's interested. And to think, it only took 26 years to find it…
I know exactly the song you are talking about… because that is exactly the song I have been looking for all this time as well. I heard it around the same time as you while I was still in high school in the early ‘90’s. I wish could help but I want to know who sang that song too.
update:
Oh word, you found it! THANK YOU!!! I have been needing this song in my life for ages
