It does not sound like suicide, it sounds like honor killing.
Two sisters committing suicide? They won’t choose drowning, pills maybe, gunshot maybe, but they are not gonna tape themselves together and jump in a river. I don’t care what race or culture they are from, it won’t happen.
BTW, if you want to kill your self painlessly. Take your car to a room, like your garage if you have one, and leave the car running while you inhale the carbon monoxide. Or if you don't have a room, run a pipe into your vehicle.
It would be a completely believable scenario if this had been Arkansas.