Since Unity 2018.2, TextMesh Pro is included with the Editor as a default package. As such, when you upgraded your project to Unity 2018.4, you ended up with a project that has (2) versions of TextMesh Pro.
The AssetStore version of TextMesh Pro is the Legacy version which is no longer being updated. The Package Manager version which is available for Unity 2018.x and up is the version(s) being supported going forward.
In order to use the package manager version of TextMesh Pro, you will need to following the procedure outline in this sticky post and to convert your project to use the latest release which is version 1.5.0-preview.4 for Unity 2018.4. Preview 5 will be out this week.
Once you are running on the package manager version, future upgrades will be much easier and handled via the Package Manager.