Is there a Paint.NET alternative?

Yes, try Pinta

Pinta is a drawing/editing program modeled after Paint.NET. It's goal is to provide a simplified alternative to GIMP for casual users. It is currently early in development.

• Homepage
• PPA

Krita is a good alternative for paint.net, for it resembles paint.net most in term of look & feel (and functions).

I worked with paint.net for years (on Win7), now changed to Ubuntu 18.04 and do work with Krita as I have been used to with paint.net

Do NOT use Pinta. While the original recommendation for this tool might have been true at the time of writing, this does no longer apply. Development for Pinta stopped in 2015, see: [Pinta] (https://pinta-project.com/pintaproject/pinta/releases/1-6)

Pinta is unstable at least for Ubuntu 18.04.

Are you looking for something like TuxPaint?