Sorry to hear about your fish. Please don't despair, a lot of shops set you up to fail. From the sounds of what you've written in your question, you did everything right.
Firstly, make sure you read about the nitrogen cycle. If you read and understand one thing about fish, this is probably the most helpful.
Secondly, get yourself a test kit. You can either get a liquid one or the strips but beware, whilst the liquid one is much more expensive, it lasts a lot longer and gives better readings. The liquid one gives you the most important reading for a new tank, which is ammonia.
From reading your question it sounds like ammonia poisoning--it's a little tricky to say exactly over the internet, but this is normally the most common stumbling block in new aquariums. Running the tank for a week won't necessarily ensure it is cycled because if there is no source of ammonia, there will be no bacteria to convert it and it may just run clean for a week. Check out this guide on cycling a new tank: https://www.youtube.com/watch?v=eBMgppmFyoE
Much of fish keeping is dealing with water chemistry. Any ammonia in the water at all will be lethal to fish.
Please don't give up with fish. They can be an incredibly rewarding pet to keep. This time, make sure you've tested the water yourself (a lot of shops don't even test for ammonia when they test it for you). Make sure you follow one of the methods in the video I posted above.
Do all your homework first before getting the fish; it can be tempting to do it sooner but it's definitely better to wait until the levels are showing correctly.