The oily film you see could be protein build up due to waste, food or plants. It is generally not harmful to your fish. It may be best for us to determine the red streaks you are talking about by posting some photos of this problem in question. As Pataflafla mentioned, it could be a natural change in color. If your betta is of blue or dark color, when they get stressed, the anal fin (section closer to body) can pale and the reddish hue become more pronounced. If your betta is transparent or light in color, the veins can be a bit more visible as well or the blood can be easily seen if they injure themselves. So not knowing exactly what you mean, photos will be very helpful in determining the problem.