Starting to go black at the edge of fins = AMMONIA BURN !
DANGER ! Your fish are poisoning themselves and will die if you don't do anything

ASAP to do:
Get a testkit: MasterTestKit for freshwater by API . While you get down to the petshop take a water sample ( half a cup full ) with you so they can test the water asap. Please post the numerical results.
Get a much bigger tank: 30 gal at least, 40 gal better.
Get STABILITY by Seachem
Get PRIME by Seachem
Get Pimafix AND Melafix by API
Get a very good filter, a pump and an airstone.
Get live plants and plenty of gravel ( best the natural, round, peasized one, instead of the artificial coloured one - avoid any sharp edges)
Set up the tank ASAP and add Stability and Prime according to instructions.
In the meantime do 50% waterchanges every day in the small tank but please add the conditioner to remove chlorine and chloramine and add the beneficial bacteria. VERY IMPORTANT.
G O O D L U C K
I keep fingers crossed your fishies make it, as this is really EMERGENCY