Keep checking water quality (ammonia, nitrates, PH) daily. Do a 25% water change every other day -- more if the levels are going up, say 33% daily. 50% or more can be very stressful for fish, so only do that if you are seeing mid to high levels of ammonia or similar very bad signs. You're looking for
zero ammonia and extremely low nitrates, ideally zero, though it is normally for nitrates to go up a bit between water changes.
What water conditioner are you using? Some city water has some ammonia in it, so you may want to switch to something like Prime which will take care of that in addition to chlorine and heavy metals, since any ammonia is not good, even very small amounts, and you'll never get rid of it all if you have it in the water used and don't neutralize it.
How long has the tank been established? It sounds like not that long, maybe not really at all. If you had high ammonia and nitrates, your tank is not properly cycled or you do not have sufficient biological filtration for the number of fish in it. Doing a "fish in" cycle can potentially take a month or more, and can be very hard on the fish, which is why it is not recommended anymore.
What brand, type, and model number of filter are you using, and what size tank / how many liters per hour of water is it rated for? When is the last time you changed the filter media cartridge?
Consider getting some starter bacteria like Nite Out 2 or similar (there are lots of options, that's the one I use, if you can't find it I'm sure there will be something available to you). Dose as it describes on the bottle for a new tank, even if your tank is older. Keep it in the fridge between doses, as this helps the bacteria stay alive and last longer.
How many fish
exactly do you have in the tank? How many of each type? How many in total? How many "inches" total? As a general rule, you should never have more than 1 inch of tropical fish per gallon of water, and ideally you want 2 or 3 gallons of water per inch of fish, more if you can afford it and have the space. There is no such thing as too big a tank for a given fish. Seriously consider getting a larger tank and higher rated filter regardless since it sounds like you have a lot for a 15 gallon, probably too many. Do a
fishless cycle on the new tank as described in the link, and move the fish to that tank once it is cycled and stable. Make sure it is stable first, or you may have the same problems all over again. If you cannot find a good ammonia source do a google search for fishless cycling using frozen shrimp from the grocery store.
A great place to get tanks cheaply is Cragislist.org -- you can normally get tanks for around $1 a gallon if you look around for a deal, which is a great price when compared with cost new, and so long as you don't buy sight unseen there is nothing much to worry about. Always clean the tank well. I'd suggest at least a 30 gallon.
Get the absolute highest rated filter you can afford to go with the new tank -- I really like the Marineland Biowheel 350 or Emperor 400 (~$30-50 online) for a 20-55 gallon, or the Marineland H.O.T. canister filter line ($50+) if you have the cash and want to keep it very very quiet (though the Biowheel filters are very quiet). Search around online, as prices vary a good bit, but buying online is normally a good idea over in store, since they can cost 2x or more locally.
Over-filtering is always a good idea. This means getting a filter rated for 2 or even 3x the volume of your tank -- I use a 75 gallon rater filter on a 10 gallon tank for example (and that had one fish in it), though you have to be careful with smaller fish doing this since the suction can be very strong. Other than the strong suction there is absolutely no downside to over-filtering. It makes for happier, healthier fish.
That's about all I can think of at the moment. Best of luck, and keep us updated. I will add anything I come up with, and watch here if you have any other questions or responses.