You definitely may have some irritation. It may take up to 5 days or so for any irritation to subside depending on the sensitivity of your skin. Makes sure you get it done by someone with a lot of experience as it will help it heal faster.
The redness, burning or tingling, and puffiness should start to go away in as little as ten minutes. There are oils that can be applied to the newly waxed area that will soothe.