I don't think its fin rot, but this is a tough call. Either way, damage has been done, and the best medication I could suggest would be "fungus eliminator" by jungle pet supplies.
Most LFS's should have it in stock. If not, you can buy it online at: http://www.drsfostersmith.com/produc...pc=1&N=0&Nty=1
Dosing this medication into the betta's water for 1 wk will help if there is a problem, yet its safe enough in case there isn't, it will work more as preventive medication. Be careful NOT to overdose, and NO SALT in the water while using this medication... there is salt in the med. You can combine this with the Methylene Blue for that week. The water will turn sort of aqua in color (blue/green), this is normal, and after treatment, a series of water changes will remove the color.
With no filter currently running, it is safe to do a 100% water change in that tank, and I actually prefer it. Bettas don't put out so much waste that bioload is a problem unless they are overfed.
A safer way to do this, and easier, is to get a hospital bowl and stick a fake plant in it for the betta to have a hiding place. Medicate the water, fill the bowl with it, and do a daily water change in the bowl with the medicated water. You can mix up to 3 gallons at a time, and it makes dosing it much easier. You can do this in a bucket with a cover, then each day, use the medicated water to change 100% in the bowl. After a week, put the betta back into his tank without the filter. The medicated water can be used for up to 48 hrs after mixing it. Longer than that, mix it fresh.
If you need dosing instructions for the bucket/bowl method, PM me, I'll be happy to help.