I agree....it looks as if hes snagged his fins on those plastic plants there.
IMO, no plastic plant is totally safe for a long-finned betta. As soft as they may feel and even with the panty hose test, there is always the risk of snagging and ripping.
Your little guy should heal up just fine with a little time, not need to make any changes so long as he is in a heated, clean environment already. But you may want to look into replacing those plants with silk or live ones to prevent any future damage.