I noticed the little white spot in some of your other photo's, but I wasnt sure if it was a bubble, something on your camera lens or on the tank, or if it was some ich/ick/white spot starting to appear.. I would keep a close eye out to see that he doesnt get any more spots appear, and that he doesnt start brushing himself up against ornaments etc in the tank..
Here is the treatment for White Spot or Ich or ick (whatever you want to call it.. lol.)
•Symptoms: Betta has white dots (looks like he was sprinkled with salt) all over his body and head, even eyes. Lethargic, No appetite, Clamped Fins, Might dart and scratching against decor
•Treatment: You can treat Ick either conservatively or with medication. Ick is a parasite. Because ick is contagious, it is preferable to treat the whole tank when one fish is found to have it. Ick is temperature sensitive: Leave your betta in the community tank and raise temperature to 85 F. Then you can choose to treat with salt or medication. Conservative: Add 1 tsp/gal Aquarium Salt 3 times, 12 hours apart so that you end up with 3 times the normal concentration. Perform daily 100% water changes to remove fallen parasites before they can reproduce. Replace the water with the right amount of salt. Do not continue this treatment for more than 14 days. If it fails or you do not want to use salt, treat with Jungle’s Parasite Clear, API Super Ick Cure, or Kordon Rid Ich Plus. If your betta lives in a jar/bowl, then it can be difficult to heat the water. There are heaters for smaller containers, but you can also float the quarantine container in a larger heated tank during treatment. Do a full water change every day and add an appropriate amount of medication to the water.
•Alternative Treatment: Personally, I have not found Ick medications very effective. I prefer to use PP to treat all external parasites. In the past, I have used 3 or 4 different ick medications unsuccessfully, and every time I resort to PP which works like a charm. Do lots of research before using PP as it is a more dangerous chemical than most.
As for the fin rot, red, or bloodied edges can be a part of it (if you read the sticky info), so it may not be septicemia, just fin rot.. Again, given his body colour, the dark edges on his fins could just be him changing colour, then again, it could be fin rot..
Personally, I would keep doing the 100% daily water changes and keep a very close eye on him for a few days, and take note of any changes in appearance, and his fins.. If his fins start to look like they are disappearing, then by all means start treating with AQ salt (if you havent already) for a maximum of 10 days.. I would also buy one of the meds listed in the sticky info. for treating fin rot.. It is better to have the meds and not need them, than to need them and not have them.
Sadly I'm no expert when it comes to fish (Betta) diseases, and find that the diagnosis is often the most difficult part of the problem.. Hopefully someone with more experience will chime in and confirm your diagnosis..
I see in your first post that you have a heater now... From personal experience, I found that the biggest cause of illness is dirty water, and insufficient water temperature (too cold) or major temperature fluctuations (usually between night and day) within the tank.. Just make sure that the heater is keeping his tank at a constant 80 deg F.