We need more info: what do you mean by "some of my website"? This is a strange statement. Have you changed nameservers or IP to point to companyB?
When you transfer a website you transfer the files first then change the nameservers to the new server, this is called mirroring. Then as it takes 48 hours for the dns change to take effect no one is seeing the site as down although there are always some minor problems even if you do mirror the site on both servers. If you haven't changed the nameservers the domain points to then this will be your cause. If you have I will update my answer.
Update after comment:
Actually if your files are on the server with company A then they are still hosting your website and your A records need to point to their server's IP. But this makes the new host (Company B) redundant.