When I went to feed him this morning, I noticed his tail seems to have discoloring... I'm hesitant to put any medicine in his tank without being sure it's something I should worry about, or if it's just him aging.
Housing
What size is your tank? a bit more than 1 gallon
What temperature is your tank? about 79 degrees
Does your tank have a filter? No
Does your tank have an air stone or other type of aeration? No
Is your tank heated? Yes
What tank mates does your betta fish live with? None
Food
What type of food do you feed your betta fish? Hikari Betta-gold
How often do you feed your betta fish? Usually about two pellets a day, and the occasional dried brine shrimp (about once a week). If he's looking more hungry I sometimes give him another pellet at night.
Maintenance
How often do you perform a water change? About every week, sometimes longer

What percentage of the water do you change when you perform a water change? 100%, besides the cup full of water I take him out with
What type of additives do you add to the water when you perform a water change?
Water conditioner -- BettaSafe by Tetra
Water Parameters:
Have you tested your water? If so, what are the following parameters? No
Ammonia:
Nitrite:
Nitrate:
pH:
Hardness:
Alkalinity:
Symptoms and Treatment
How has your betta fish's appearance changed? His tail looks discolored, almost blotchy, with translucentish spots.
How has your betta fish's behavior changed? He does seem to be spending a tad more time at the bottom of the tank, but he's still as energetic and interactive as ever when prompted, and will swim around for food and when I interact with him. I contributed his time at the bottom earlier to the removal of one of the plants that used to be in the bottom corner of his tank. I took it out to see if he liked the space to swim more. Don't worry, he still has a nice faux silk plant with big leaves in another corner to hide in.
When did you start noticing the symptoms? This morning, but he could've had it for a day or two and I just not notice.
Have you started treating your fish? If so, how? n/A
Does your fish have any history of being ill? No
How old is your fish (approximately)? 2+ years (I'm not sure how old he was when we got him, but I've had him since Fall of 2010)