Frayed fins can also be a sign of high ammonia levels in the tank. Check your water parameters to find out where you stand, BEFORE you start adding medications. It ammonia levels are high start doing 50% PWC daily until it is under control. You may need to use some Seachem Prime if they won't come down.
If your levels are OK, it may be fin rot. I'd bet that since your tank isn't cycled yet, they probably aren't.
Fin rot IS usually brought about by poor water quality (high nitrates), which in turn stresses your fish. Once stressed they become susceptible to bacterial infections. This kind of infection is caused by gram-negative type bacteria.
If you catch it in the early stages, a teaspoon of salt/gallon of water can help stop it. Otherwise you'd need antibiotic treatments with products like Maracyn II, bettafix, Jungle Fungus Eliminator or Tetracycline. Don't use regular Maracyn, which is used against gram-positive bacterial infections. That is what your good bacteria are and you don't want to kill them off now! If you have to treat the tank, do it after your water changes. Be sure to remove any charcoal from the filter while treating the tank with medications.
Make sure that you are treating the right thing. i.e. ammonia poisoning or fin rot. You have some time yet if it is fin rot. Don't throw medications at it in the hopes it will go away. Be sure of what you are treating first.