Fin rot does not transmit to healthy fish. Poor water chemistry usually does the trick. Your fish are probably stressed and their immune system is weakened. That doesn't necessarily mean ammonia, although that is most commonly the case; it can mean that your water may be too hard as well, or that the temperature is too low (ideal is 80F). How often do you do water changes? Keep in mind that you should do 100% water changes on a 1 gal bowl at least twice a week (as a reference). Adding a little aquarium salt to the water may help as well (half a teaspoon per gallon).
Hope your fishies get better soon!
Here's a link with great info about fin rot: