InDesign only links to external images, unless as @Yorik points out in comments, you are pasting images into the InDesign file. Which is a bad idea.
13mb is really not large at all. Even with only reference links, it's fairly easy to hit 13mb for an INDD file in roughly 20pgs.
Saving as an IDML file (InDesign Markup Language) might reduce the file size. An IDML file is merely a markup data file that InDesign can read and then regenerate the layout based upon the markup. Unlike an actual .indd layout, the .idml data is typically much smaller in terms of file size. One simply must have InDesign to utilize an .idml file.
If an IDML file works, images won't typically "automatically" relink.
But it's easy enough to relink images to a folder....
Or you can archive the .indd file in something like a .zip archive. Which should reduce the file size. But there's no telling what any size reduction may be without actually archiving the file. (One should be "zipping" InDesign files when emailing them anyway. Sending raw InDesign files through email will often result in file corruption due to common email server virus scanning.)
There are also file transfer services such as DropBox, Hightail, GoogleDrive... which would allow for larger file transfers and circumvent the 10mb limit found on many email servers.