It sounds like your birthday cards are really special to you. There’s nothing wrong with saving keepsakes, but setting boundaries for them is a must.
First - Allocate a space to save the cards and keep your collection contained within that space. Choose from containers such as Photo Boxes, File Boxes or Accordion Files. They’re easy to use solutions, are available in multiple sizes and cool colors and prints that work with any decor.
The rules to play by: 1. If you don’t touch the cards for several months, it might be time to re-think how important it is to keep all of them. 2. If the allocated space or containers start filling up, implement the “one-in, one-out” rule and stay within your limits.
Maybe some day you’ll just keep the really special cards. You’ll always have the memories of how great they all were.