I second what LMF says and I just want to add that while cycling, you will need to change their water every day.... So there's 2 things you can do as a great start:
1) Read up on cycling a tank - it's invaluable when starting to keep new fish
2) Do a massive waterchange straight away making sure the temperature is matched and a dechlorinator is used.
Sadly, no medication will work while your water quality is stressing your fish, if anything, it can push them over the edge

... so the most important thing right now (in the absence of test kits) would be daily water changes using temperature matched, dechlorinated water.
Do the white specs look like grains of salt? If so, then they may have ich but will wait for you to post back on this.
Are you able to invest in some test kits? This will help you understand what's happening with their water and control their environment - so that they can thrive in a healthy environment. PH in particular is a very important test to have on hand. When fish are exposed to ph swings, it can make them very ill so having a good handle on your levels is a great start...
If you have any questions, just ask - there's so many great people here just waiting to help you through this first stage of fishkeeping
And a big welcome to you from me also