"apt upgrade" (unlike "apt-get upgrade") does pull in new packages, but it won't remove existing ones.

I don't see why "apt upgrade" wouldn't install the new kernel. It's hard to tell what when wrong without knowing any details.

Anyway, if apt decided to hold back a package for some reason, most of the time you should be able to install it with "apt(-get) install". Do not install packages with dpkg unless you know what you're doing.