404 errors with new WP 4.4 Via Bluehost

I had a wordpress site with no outside host. I signed up for Bluehost, downloaded WP4.4. via BH. I had to rebuild my site (new theme etc) it’s fine but now if I search “the idiot croissant”, I get results for my old page and old posts but if you click it, you get Bluehost 404 error. If you type theidiotcroissant.com on top, it takes you directly to my new site.

Am I missing something here? My blue host NS1 and 2 are okay. I’ve tried everything, including crying. Nothing seems to fix these old links. I can still access my old post via the old WP dashboard. I have to login to ADMIN to see the new site and 4.4 version dashboard.
Should I load those old post onto my new site? I didn’t want to do that. I assumed not including them on the bluehost version would make them disappear from google searches. I just want to clean things up so people can find my site. Note, I have paid WP for mapping on my theidiotcroissant.com and I told wordpress to drop the /wordpress but it still shows up in google searches.

Sorry for all the questions, but I’m new here and this thing is not very intuitive.