Expanding a little on what wisecracker has already said....

It looks like you are trying to use ANSI terminal escape codes, but they start with an <escape> character; not with the character <3>. Furthermore, you haven't told us what shell you're using and the behavior of echo -e varies considerably from shell to shell, from operating system to operating system, and even if you use the same shell on multiple systems, the behavior of echo -e may vary even when echo is a built-in utility within a given shell.

Using printf avoids the various behaviors of echo and the changes to your color introducing variables can be fixed by replacing the leading 3 with \033 (i.e., the ASCII escape character). In bash you can replace the \033 with \e. In ksh93 you can replace the \033 with either \e or \E. These uses of \e and \E can be used to reference the <escape> character even when you're using those shells on a mainframe that uses EBCDIC instead of an ASCII based codeset. (But you probably won't find terminals that accept ANSI terminal escape codes on a mainframe.)

Note also that it is usually considered to be bad form to write these escape sequences into a file unless the file is associated with a terminal device. For example, on systems where you can tell the ls utility to use various colors to indicate various types of files, it only does that when standard output is directed to a terminal device file. If you redirect the output of ls to a regular file, it won't output the escape sequences to produce those colors.

Code:

GREEN='\033[0;32m'
RED='\033[0;31m'
WHITE='\033[0;37m'
RESET='\033[0m'
FILE="/usr/share/sounds/My_Sounds/Short_doorbell.wav"

if [ -f "$FILE" ]
then
     printf "${GREEN}File exists.${RESET}\n"
else
     printf "${RED}File does NOT exist.${RESET}\n"  
fi

For other ANSI terminal escapes (such as bold, underlined, and/or crossed out text and cursor motion and blink rates see ANSI escapes codes in Wikipedia.