It’s “relatively” easy to publish on Medium, but “easy” depends on personal circumstances, like what you are describing.
You can publish from your phone as an “article” that would be associated with your profile. If you want to publish to a publication, you will need to work from your desktop. You would also need to apply to the publication to be able to submit a draft from within Medium.
How difficult is it for you to work from your computer vs your phone so I can offer next steps?