Hi Tara,
Since you already placed a 301 redirect from the old post to the new one, then you're all set and there is no need to delete the old posts because as soon as you, or a crawler, access the old page,s you'll be redirected to the new ones without "seeing" the old content.
If you are referring to deleting the content from your CMS, then you can go ahead and do so as they are not accessible anymore. Just make sure that the 301 redirects are still in place.