Read up on Fish In Cycling. Your tank needs to build up colonies of beneficial bacteria, BB, to handle the fish waste.
What happens in a new tank that is not cycled, when the fish poops it builds up and you get large amounts of ammonia. The ammonia is very damaging to the fish and that is probably why your fish is sick. It's not your fault , stores often don't give very good advice on how to start new tanks.
If you're going to the store anyway you might consider picking up a Java fern or Moss ball or easy plant to put in there. The live plant can also help with the cycle.
Yes, I agree do a large water change right away. The new water out of the tap you want to make sure matches the temperature of the tank water. And you want to add dechlorinator , I use prime, to the tap water in the bucket before you put it in the tank.
As was mentioned, if you do not have a heater you will need to purchase one. Bettas, especially ill bettas, need warm water. Normal temperature when the fish is not sick would be about 80°F.
Be careful just throwing medicines into a tank. Try to identify what is actually wrong with the fish, whether it is fungus, or Ich. Heat and some salt can help. Ich looks like grains of salt on the skin of the fish. Fungus may be white but usually has fuzzy edges and fungus can vary in size.
The most important thing right now is to get the fish into clean warm water and try to support the fish. Test your water or get your water tested. The most vital things you're looking for right now are ammonia and nitrite and nitrate levels.
If you buy Prime, you only need to use two drops per gallon of water.
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