Hey @cinziaccc! Welcome to the forums!
I BELIEVE this is very possible.
So first, you need to have a texture FOR your sun to replace the old one. If you have that, go into your level and in the world outliner find your Sky Atmosphere (or Sky Sphere). With that selected, look at the details panel which is on the right side of the editor by default.
Next you want to find the Sun texture property and put in your custom texture. 
Hope that helps!