What did you use for texture? Usually if texture feels dry and does not rub off on your hands, you can paint it. Be aware that you have to prime it first, and I would use either Zinsser's Cover Stain (oil) or their Bulls Eye 1-2-3 (latex).
Example: I removed the popcorn from the ceiling of my home office, after taping plastic over the walls; sprayed on aerosol texture; primed and painted all in one day.