When changing to SSL, be sure to edit your wp-admin > Settings > General > WordPress Address (URL) and Site Address (URL) values to include https.
If still having troubles the media items (I believe) are built with site_url or home values (mentioned above) in _options. Verify they’re https, then check out if you have a value in upload_url_path, if so verify its set to https.
If nether of those things work, within your database (presumably with phpmyadmin) check to see in _posts what the guid value is of a specific media item is (where post_type is attachment). If those are http, you can update them in to https with a script like:
UPDATE `_posts` SET `guid ` = replace(guid, 'http:', 'https:');
(always back up your database before running a query like that!)
When moving to SSL, its also recommend that on your Apache/Nginx server, you setup a redirect that forwards all http requests to https before the code is reach, this saves a lot of work and makes life a lot easier (there’s thousands of how-to for that online).