CCW has nothing to do with OC. Yes, you can still OC.
You lose no rights by getting a CCW. This would be like saying that once you get a driver's license, you can no longer walk down a street.
Unfortunately, many people hand out misinformation either through ignorance, or outright deception. LEOs and firearms instructors are frequentlyamong the worst offenders. When someone tells you "it's against the law", ask for the statute number.