Hi Beth!
Loved reading this beautiful poem :D
So here's how you can reach more readers on Medium.
1. Use tags. When you write a story, you will see three horizontal dots in the upper right corner of your screen. Click those dots and a drop down menu will appear. Click "Change Tags." You can add up to 5. Tags like "Poetry," "Poems on Medium," "Love," "Beauty," "Short Stories" are popular examples, but feel free to get creative.
2. So for online publications on Medium. First, take a look at this website: https://medium.com/the-smaller-m/a-list-of-poetry-publications-on-medium-b16afed0dec7''
They have a list of top poetry publications (but you can also do a Google search "poetry publications on Medium." Most of those publications will have submission guidelines when you look at their specific website/profile. Follow the instructions to be added as one of their writers. This might take a few days or up to two weeks.
When you have been added as a writer, you will usually get notified via email.
After that, you would click those 3 dots on the upper right corner of the screen again, and this time, click "Add to Publication" and a publication will appear (that you have been accepted to). An editor will review it for content and spelling/grammar and (usually) accept it within a week. It's a bit of a longer process, but publications will put your work in front of hundreds to thousands of readers (potentially). So it's 100% up to you. Sometimes I submit my work to publications, sometimes I don't.
3. Add a featured image (before the text) to draw a reader's eye into your work. I use either Pixabay or Unsplash.com for free images (I also give credit right below the image). Just copy/paste it to your poem.
4. Under those same 3 dots is "Manage Unlisted Setting." Aka money/royalties. It won't be much, usually adds up over time. But it's something :D You will see "Make this Story Unlisted?"
No = Money (public for everyone to see)
Yes = No Money (No one will see poem except you)
Hope this helps!