Very likely it is fin rot. Sounds like classic fin rot. Fin rot doesn't spread, but it occurs when you have bad water chemistry like high ammonia and such - in other words, do a nice water change. It's usually bacterial, so you can use an anti-bacterial to try to help clear things up, but normally, with fin rot, if you get your water clean and keep up with it, it should just clear right up.
But, if you leave it, it will start affecting your other fish - perhaps not with fin rot, but with other illnesses due to their immune system breaking down from poor water quality.
for more information on fin rot and other water-quality-related issues, I usually do a google search on that specific issue and for whatever fish - there's tons of great information out there! What I'm giving you is info I recall from when I used to keep mainly bettas in unfiltered bowls.