My Cleo has the same thing, few spots on his pectoral Fin( haven't noticed any white lines though). I'm not quite sure what it is, but part of his pectoral fin has fallen off while he has been in QT.
.I have been watching him in his 1 gallon QT. for 2 weeks and they haven't moved onto his body anywhere else just his pectoral fins. hmmm...I hope you find out what it is! I plan on getting some sort of anti-bacterial and parasite medication at petco today if they have any.Hopefully it will do something, have already wasted money on bettafix,fungus clear and 3 in 1 treatment tabs... all of which have done nothing, and the fungus clear made my fish act real sick!