“The nvidia driver built a new version of the kernel” is a little surprising. I’m not sure how this will be interpreted on this forum, but my best advice is to not use the .run file driver installer if at all possible. This is something that tends to trip up people who are coming to Linux from Windows, who are used to having separate installers for individuals drivers and programs, and it’s really not a sensible way of doing things when you a Linux package manager you can use instead. The only companies that even package Linux software with executable .run installers are generally those that maintain Windows code and are just used to doing it that way, and it’s almost always going to introduce more complications than necessary (like your new kernel).
Generally, Nvidia drivers, being proprietary, will not in the default set of sources configured by a given distro’s package manager, so you’ll need to add some additional repos. In Ubuntu, these come in the form of additional PPAs, which you can add via apt-get at the command line, or in the synaptic package manager. For Nvidia drivers in Ubuntu, there’s this new semi-official PPA, which was created specifically in response to too much confusion as to how they’re supposed to work:
As well as this other one I’ve been using for a while, that looks like it’s just been deprecated in favour of the new one:
I can see the argument for “I’d rather get something directly from the vendor rather than through some guy who happens to maintain a build pipeline for Ubuntu,” but trust me, Linux is all about the package manager. For example, I have no idea how to advise you on removing the driver version you installed via the .run file; if it were installed via the package manager, it’d be a simple apt-get remove xyz.
Hope that helps!