It's not okay that he is sticking against the filter. You should attach a thin and porous sponge over it so he can't be injured.
He's clamped which means he is showing signs of stress. The tips do look black/brown to me. Do they also to you?
What is the temperature of the tank and what water conditioner are you using?
Make sure you only leave the lights on 8 hours during the day and always have it off at night.
Also you should read this guide on fish-in cycling: http://www.bettafish.com/showthread.php?t=47838