Surprisingly in the newest version of Blender 2.81 I can not draw in Texture Paint. It doesnt just draw on mouse pushing. And also it doesnt have ‘Tools’ and ‘Options’ sections sidelong of the window which other users` Blenders have:
Texture painting for 2.8 is still a wok in progress. Many of the common tools have been put in the top bar, but for all the tools, open the N-panel (press N) in the image or 3D window, and chose the Tool tab. As for drawing, I have run into the same problem. I’m not sure if it matters, but make sure you have created an Image Texture in the object’s material and have it selected before going to the Texture Paint workspace. You appear to have done this, though.
There are other issues with the process I won’t bring up, but will say that if you are comfortable with the 2.79 version (and happy with the results), maybe keep using it for this task.