Blue shift (aka increased apparent frequency) is caused by the velocity between you and the source, not the velocity of the source. That is how the speed of light works in General Relativity. If you move toward a photon is doesn’t get faster, it gets higher frequency. If that’s in the visible range it shifts toward the blue end of the spectrum.

If you move fast enough, all of the ultraviolet light coming from behind you becomes visible light. A little faster and all of the ultraviolet light in front of you becomes X-rays. And all of the hard x-rays become gamma rays.