You can never really "catch up" on lost hours of sleep. But what you can do, going forward, is prioritize what you are doing in your waking time so you can try to get the proper amount of rest for the days leading up to your big day. I don't know what you do for a living, but can things at work be put on hold or delegated to a helpful coworker so you can leave work on time? can the unpacking in your new place (congrats by the way) wait until after the honeymoon? Also do as another bride here suggested and make a checklist so you can keep a clearer focus on what needs to be handled for the wedding day. Can your fiancee/friends help with any of it? When a person is tired/has the puffy eyes, it sometimes takes a few days of healthy rest to relieve it so try, try to take the opportunity now to start so you feel your best on the wedding day.
PS: Save this email for me when mine is coming around so I can recall my own advice.