find, you should use a way that is safe regarding spaces and other funny symbols that can appear in filenames. This should do (provided your
du versions accept the options):
find . -type f -user "$USER" -print0 | du -ch --files0-from=-
-c option is to have a nice total at the end). This will not count the size of the directories though.
If in the directory tree you have some directories that are not accessible by you, you might get some junk (permission denied) on your screen, so you might want to redirect
find . -type f -user "$USER" -print0 2>/dev/null | du -ch --files0-from=-