Yes you really need to get the test kit for us to be able to give you the best help
I know it costs to buy one of your own but think of all the money that you're wasting with fish dying. It's better to have it on hand. The very first thing I do if I suspect a problem in my tank is to run a full test panel (then I do a water change)
OK, prepare yourself for the question barrage but this is how we can best help you, by asking for more info:
Was the water "fine" according to Pets at Home before you added the new fish, or after?
What does "fine" mean to them, do you have any idea? (get a kit
)
What were the new fish that were added? How many?
So it's the fish that were only in there a week that died?
Have any of your older fish died?
What kind of filter do you have?
How did you acclimate the new fish before putting them in your tank?
+ all the questions Caliban asked
Hang in there