WP-Mix

Here is a good, WP-API method of limiting post display to the currently logged-in post author (i.e., so users can only view their own posts). Here you’ll find two variations of this technique. The first limits the display of posts for non-admin users only. The other limits the display of posts for all users, including admins.

Display only posts from logged-in post author (excluding admins)

To restrict the posts that each logged-in author can view on the front-end, add the following snippet to your theme’s functions.php:

// limit post display to post authors (excludes admins)
function shapeSpace_set_only_author($query) {
	global $current_user;
	if (!current_user_can('manage_options')) {
		$query->set('author', $current_user->ID);
	}
}
add_action('pre_get_posts', 'shapeSpace_set_only_author');

Here we are using pre_get_posts to modify the post query, such that only non-admins will be able to view only their own posts. So it will allow any admin-level users to see all posts, while all other users will be able to view only the posts for which they are the author.

Display only posts from logged-in post author (including admins)

We can modify the previous technique to limit post display for admin-level users as well. So all users including admins will only be able to view their own posts. To do so, we can remove a couple of lines, like so:

// limit post display to post authors (includes admins)
function shapeSpace_set_only_author($query) {
	global $current_user;
	$query->set('author', $current_user->ID);
}
add_action('pre_get_posts', 'shapeSpace_set_only_author');

Make sure to test well, all cases (logged in, logged out, different users, etc). Should work fine as-is, but you need to mindful of any other related things that your theme or plugins may be doing. Should definitely be enough to get you going in the right direction.