I have chromium installed. I want to update it and only it. Is there any way to do that?
Will actually perform an update instead of an install.
Keep in mind that changing from one version of an package to another is still considered an "install" in dpkg terms. It's only us humans that see it as an update.
As EliahKagan has pointed out, updating chromium will also update its dependencies, where needed.
A (somewhat cumbersome) way to do this would be to have the Update Manager set so updates are not installed automatically, and then uncheck every listed package in the available updates except for Chromium.
Just keep in mind that updates in stable Ubuntu releases are provided to correct stability and security bugs - by not installing them, your system could be less stable or secure than it could be.