White spots, bigger than ich...
It could be a fungus, are the spots slimy-looking or fuzzy?
Of course it could also be a very bad case of ich...those white "freckles" tend to run together after a couple of days...
Just so you'll know what ammonia poisoning does (for if/when you ever have to recognize it): Your fish will gasp at the surface, their gills will be inflamed and red looking, and they will not eat normally. Ammonia basically puts caustic burns on their mucous membranes, like you had poured lye or baking soda on them. Diluting the ammonia is the only way to cure this, and only if you take care of it quickly.
As for your spot problem, try raising the water temp. to around 82 or so, and add a little aquarium salt to your tank. If it's ich, it will speed up its life cycle and the spots will "fall off" within a couple days (you still have to treat the water or they'll come back. The spots are the parasite in its cyst form, they have a free-swimming stage also). If it's fungus, it will start to clear as well. Do a google search for fish disease id and see if you can find a pic that looks like what you have (or snap one yourself and post it, and we'll take a guess).
Good luck!