I've heard that tea tree oil is actually bad for Betta's as it coats their labryrinth lung (the one that allows them to breath air) and can cause them to drown.
Also a 1/2 gallon is too small and you would need to do more frequent water changes. Here is a helpful thread on water changes - note that 1/2 gallons are not listed as they are considered too small: http://www.bettafish.com/showthread.php?t=115758
Also, it sounds as if his tank is not heated, they are tropical fish and need to be in minimum of (depending on who you talk to) 74 to 76, warmer when they are sick. Room temp is not ok for Bettas, especially sick ones.
Please fill this out so people here can help you better:
What size is your tank?
What temperature is your tank?
Does your tank have a filter?
Does your tank have an air stone or other type of aeration?
Is your tank heated?
What tank mates does your betta fish live with?
What type of food do you feed your betta fish?
How often do you feed your betta fish?
How often do you perform a water change?
What percentage of the water do you change when you perform a water change?
What type of additives do you add to the water when you perform a water change?
Have you tested your water? If so, what are the following parameters?
Symptoms and Treatment
How has your betta fish's appearance changed?
How has your betta fish's behavior changed?
When did you start noticing the symptoms?
Have you started treating your fish? If so, how?
Does your fish have any history of being ill?
How old is your fish (approximately)?