Did you mean 160
PPM (parts per million) of nitrate, or did you mean 16.0 ppm? If it's 160, that's waaaay over the top for a cory, and probably a whole lot over the top for your guppies. If it's really 160 ppm, that's probably the main reason for your cory's decline. They're sensitive to nitrates and mostly need nitrates at less than 20 ppm, AFAIK.
I agree that you should ask your mom to buy an API Master Test Kit for you and your fish. Fast! No time to save up allowance for it. Maybe she'll give you a loan. The strips aren't reliable, and with the Master Test Kit, you'll know what's really happening in the tank.
Check your tap water for nitrate, too. Won't do much good changing water if it has high nitrates, although that would be way over EPA standards (which I think are 10 ppm maximum but can't remember exactly). If you use municipal water, the provider can get fined big-time if it exceeds EPA standards, and they are surprisingly highly regulated.
If you have been doing regular water changes (that's a big *IF* I can't determine) and the nitrates in the tank do indeed show up as 160 ppm by a more reliable test kit, and if the nitrates in your tap water are over the EPA standards, then you should report it plus start using bottled spring water for your water changes in the interim.
Good luck. I can't tell if your Cory or other fish made it or not. Hopefully it will all work out fine, although I hate to break the news but don't hold up out much hope for the Cory from what you said.
You obviously care deeply about your fish. Keep up the good work by researching and additionally asking questions here. We're here for you!