Could it be:
Rain
I come from a cloud.
Clouds are made of water which will fall down as rain.
Some long streaks of light And a glowing shroud.
Clouds (the shroud) can glow, and sometimes when they have holes, you see streaks of light come from them.
But now out of sight.
As rain in the sky, it is not easy to see in comparison to clouds.
Seen in the summer,
It can rain quite frequently in summer (depending on your location)
Despite my nickname.
A possible reference to 'reign' a homophone to rain.
Many deaths occurred,
Many deaths can occur from floods (or excess rain), or the reign of a bad ruler.
But I'm not to blame.
I guess we just have to blame mother nature!