I am not sure we would say 'my hair got sunburnt' (I speak British English, so use sunburnt - Americans would say 'sunburned', as Phil pointed out - either one is fine). I would more likely say 'my hair has been bleached (which means that the colour gets taken out) by the sun'. As all four of your sentences are essentially saying the same thing, I would suggest the following as one way of expressing the idea you want to convey:
Since coming here my hair and skin have been badly damaged by the sun.
Ai - not sure if this is a theoretical sentence or it is referring to you - and I don't know where Cali is, but as an Australian, let me give you some advice - wear sunscreen, sunglasses and a hat, and stay out of the sun during the hottest part of the day!