Aww.. Don't feel bad about it really =/
I know you must be suffering a lot for your loss but at least was a quick death than leaving her to die in her tank.
I bet she knows you tried your best to ease her pain, so you should at least feel relieved that she's in a better place now. =]
Don't read if you can't handle "gore"-ish stuff.
Might be a bit off topic but I remember once when I was around 10, we went to one of those fishing clubs, they had small ponds we could fish the whole day, if you wanted those fishes you could just put on a box or something and they would charge you for him and that's it...
Well, I used to LOVE fishing, I still miss it, but I feel so sorry for the fishes that I don't do it anymore, but anyway;
In the end of the day at the cue for taking the fishes home (to eat), I saw them opening the fishes, cleaning their skin and everything while they were still alive!
I wasn't taking any fish home, but I remember I ran to the guy and yelled at him almost crying "Sir, sir, those poor fishies are still alive! They are feeling pain, can you kill them first, please?" The guy just thought it was cute of me and smiled, then replied "They don't feel pain sweetie" then I saw the fishes without any organs inside still breathing and looking at me scared for their lives... Still gives me the chills remembering it. >_>!
Anyway, you gave your poor betta a quick death, the range of being alive after the decapitation is for 5 seconds most in the head only. So yeah, don't feel bad, I think decapitation is better than the freezing technique in my opinion, but yeah, you need to "cold-blood" kill it. :c
That's me on the photo alright.