It's not only unfair to you and your ex, but it's unfair to that new person to continue keeping, um, like you were before. You also don't want the new person getting suspicious of you, so you just act like another person your ex knows (even though this won't work because the new person has probably stalked you to death and knows everything about you anyway -- but that's another story).
You wave from afar, minimize giggling and refrain from having casual texting conversations.
And once I realized that I had that new person and my ex had moved on, I felt that it was okay to officially move on myself." Instead: Spend time with the important people who are already in your life.
Talk more with your family and reach out to friends.
During your post-breakup period, it was easy to push your limits with your ex, whether it was with those drunken hookups, calling him or her late at night "just to talk," laughing together at parties or joking about the silly or embarrassing things that happened in your relationship.