Is there a way of telling? Maybe a difference in music?
You have no definite way of telling. This is kinda why shiny hunting is so hard.
This said shiny fishing is the easiest way of getting a shiny because all you have to do is fish over and over again. As long as you get a Pokemon on each rod swing and you don't lose it, your chain still goes on. Get a Pokémon with the "Suction Cups" or "Sicky Hold" ability in the first slot, fish in a "corner" (where you block the only square to get out of there) and you should have a pretty good chance to satisfy this condition.
The best way you have to know is to keep fishing until you do get a shiny.