No, you should not. Most people swirl their whiskey because they have seen people swirl their wine to see the “legs”. Those tear drop formations on the side of the glass are actually alcohol adhering to the glass as it evaporates. When you swirl your whiskey, this alcohol evaporates faster and emits more of a hot or burning smell. This kills the natural aromas of your whiskey that you would normally smell if you had not swirled it.
Keep your glass still before raising it to smell the whiskey. Keep in mind that most of your smell is in the back of your throat so as you smell your whiskey keep your mouth slightly open and you will be surprised at the little bit extra that you get. One last thing to mention when nosing your whiskey, just raise your glass to the bottom of your upper lip. There is enough aroma to take in from there without overpowering your sense of smell.