Instead of
echo $input"$input"
try
eval echo $input"$input"
It's not even bash-specific, works on /bin/sh!
Note that this poses a serious security risk because eval just executes what you give it. In this case, the shell interprets the string $input as $test, and then eval executes echo $test. But what if the user entered $test; rm -rf *? eval would be presented with echo $test; rm -rf *. Be very careful if you do this.