Try Google Drawings. I have great high school memories doodling with friends in class on PC. Its live-synced, names are color-coded, and all edits (revisions) are stored and undoable. You get to take advantage of Google's phenomenal servers, so everything loads rather quickly in my experience.
Docs on mobile may be just for text editing - I did a little research and found there is no Google Drawings app. For this to work without PCs, you need to open Google Drive in your browser and force desktop site (in chrome tap three dot menu and check "desktop site" box). Then, if you can get a handle of the unwieldy(small) UI everything should run smoothly. I believe this will work cross platform as both OS's support HTML5. This may be your best choice.
I'm looking for a social drawing app myself, so if you find anything good, let me know! I'm particularly interested in the concept of an infinite canvas that is live updating and publicly shared. Malmal early access on the play store is pretty cool but lacks the polish that time or a larger development team would offer.