I'm asking for a world I'm making, which orbits a red star.
According to this image, there is a star that would make the sky white.
What would the sky look like during sunrise and sunset on a planet orbiting that kind of star?
What you are calling a red star is most likely a red dwarf star, probably further along the classification, because a M0 red dwarf will produce a pale whitish blue sky on an Earthlike planet. So to get to white sky it might be, say, a M5 or M6 star.
The reason the sky looks white is the light from the star contains a lot more red light than the light from our Sun. The blue colour of Earth's sky is due to Rayleigh scattering and because blue is shorter wavelength it gets more scattered than colours like red. the result is the blue colour smeared evenly across the sky, so the sky looks blue. With a M6 red dwarf its light will contain more red and since both red and blue are scattered the planet's sky now looks more whitish probably with a underlying bluish tinge.
At sunrise and sunset because there is lots more red light the sky of a planet orbiting M6 red dwarf star sunsets and sunrises will blaze with reds, scarlets and crimsons. They should be magnificent.
This answer hasn't discussed the role of particulates in the planet's atmosphere and has only dealt with the effect of Rayleigh scattering on a clear sky. More information can be found here.