Definitely sounds like a 301 redirect issue. As in you didn’t do that when you launched your new site, so Google is trying to index the pages it knows about on your site and can’t find them, after awhile they will remove those old pages from their index. In the meantime, they will get around to indexing your new website, but it could take up to a couple of weeks.
If you had rankings before, you definitely need to 301 redirect right away as that will pass the old link juice along to the new pages. If you don’t do that, you have to start from square one getting your website to rank again (at least as far as backlinks goes).