Possible Fin Rot?

[Purple]

Housing
What size is your tank? 1 gallon
What temperature is your tank? Unsure. Upstairs (where the room where she is at is) stays at around 78F, but the room she is in is usually a few degrees warmer. (I sweat if I do much in the room)
Does your tank have a filter? No
Does your tank have an air stone or other type of aeration? No
Is your tank heated? No.
What tank mates does your betta fish live with? None

Food
What type of food do you feed your betta fish? How often do you feed your betta fish? Used to be two Aqua Culture betta pellets once a day. A week of fasting (constipation), then a pea on Saturday (1/2), then part of a frozen brine shrimp cube by Hikari and a pellet Monday, and today she's had part of the cube and I'm probably going to feed her a pellet tonight before bed.

Maintenance
How often do you perform a water change? About once a week, but I did both Saturday and Sunday (Sunday is cleaning day)
What percentage of the water do you change when you perform a water change? 100%
What type of additives do you add to the water when you perform a water change? Tetra "Aqua-Safe" dechlorinator and conditioner (no additives like color enhancer or whatever that I know of)

Water Parameters:
Have you tested your water? If so, what are the following parameters? N/A

Ammonia: ?
Nitrite: ?
Nitrate: ?
pH: ?
Hardness: ?
Alkalinity: ?

Symptoms and Treatment
How has your betta fish's appearance changed? There is a small chunk missing from her anal fin. The edges are light gray and there's a white hair-like thing hanging down that is about the length that her fin usually is. A little dent near the back of her anal fin is just now appearing. The edges of her anal fin are a little lighter than usual. Her back fin clamps more than usual, but it doesn't remain clamped for long. It has only happened a few times.
How has your betta fish's behavior changed?A wee bit less energetic than yesterday and the day before, but that much energy was a bit out of character for her.
When did you start noticing the symptoms? About ten minute ago. Dent appeared while writing this.
Have you started treating your fish? If so, how? By the time someone replies, I will have probably given her a 100% water change.
Does your fish have any history of being ill? She had mild Ick when I first took her home from my boyfriend's house. It went away very quickly.
How old is your fish (approximately)? 6-8 months. She's small and really energetic.

[Canuck Fins]

With a 1G tank, you need to changed the water daily. The ammonia will build up quickly leading to fin rot and ammonia burns. Fin rot will make the edges look blackened. Are the edges around the missing chunk black?

[Purple]

No, the front chuck is really light gray. The back just looks like someone cut a piece of her fin.