If you want to do it as correctly as possible you need to craft your URL properly. The previous answer which uses string concatenation isn't wrong, but a better way might be:
return Redirect::to(URL::to('uploads/show', [$id]));
You will find though that as you get more routes, and especially the first time you decide to rework your routing convention, that using named routes (or at least controller-based routing with Route::controller) will probably serve you better. In this case it's a similar situation:
// routes.php
Route::get('uploads/show/{id}', ['as' => showUpload', 'uses' => 'Controller@action']);
// redirect:
return Redirect::route('showUpload', [$id]);
Also notice how you can pass the params directly in here (rather than using URL::to()) as using a named route isn't a simple string route like above.
Similarly, if you were using controller-based routing:
// routes.php
Route::Controller('uploads', 'Controller'); // I don't use this, syntax is like this
// redirect:
return Redirect::action('Controller@getShow', [$id]); // again I don't use this, but it's similar