How your room would light up if you won't shift the curtains aside and let the sunshine come in.
Is the word shift correct when used about curtains in this context?
In your sentence, shift is used in the following sense:
b : to make a change in (place)
I shifted the bag to my other shoulder.
To expand on the idea, what you are actually doing is shifting the end of the curtain from its location on one side of the window to the other side—which also shifts all other pieces of the curtain along the way. This exposes the window behind it.
Such a term would not be misunderstood. Although, as said, there are also other terms. The most common is likely just open the curtain.