Couldn't really see from your photo, but it may very well be fin rot. Yes, it's very contagious. And yes, you should quarantine him. There's a lot of meds out there. Try your lfs. Hope your guy makes it. One of my boys recently got fin rot and he's barely hanging on.
If you look behind the tail in front of the plant on the right, there are about 4 or 5 tail pieces hanging on by a thread. That's what I'm looking at.
Here is a picture of him just 3 days ago. This was taken Thursday night. So something has obviously happened to his tail fin. Can fin rot do that to a fin in just 3 days? His tank mates are 5 White Clouds and 4 corys. I have never seen him get nipped.
Fin rot works fast, my friend. My turquoise vt, Usurper, was doing great. Then I wake up one morning with more than half of his tail gone. The night before that, he showed no symptoms whatsoever. Scary sh*t.
Hope I did it right. This was my first attempt at posting pics here. I see them.
Anyway, I got my Betta in the bowl we had him in before we got the community tank. And I got some meds from the store. I'll keep the forum posted on how he does.
I get home today and the Betta had ick and a White Cloud in the tank the Beta came from was dead. I ran out to the lfs to get some meds for ick and when I got home one of my corys was dead. It's now a couple hours later and the Betta is dead.
I'm sorry to hear that. I've gone through the same thing last week and now all my bettas are quarantined. One just died earlier from fin rot, and another one's soon to follow. One of them still has ich.
I'm sorry for your loss, but the quicker you move on the better. Clean your tank, quarantine your fish for a while. Treat them for any possible illness. Then rebuild your tank. And buy a strong, healthy betta. Cheer up.