The wordpress.com free plan doesn't give you control over which image becomes the og:image Open Graph meta tag on the pages and posts you've created. The tag is important because it's used to show a preview image for your page when it's shared on social networks like Facebook and Twitter. If the image is wrong it will confuse the people who want to share your page.
To see what the default preview image is for any Wordpress page or post you've created you can paste its URL into the Facebook debugging tool.
If the image isn't the one you want, there's a workaround to change it but stay on the free plan. Disclaimer: this workaround is based on trail and error from editing the Victorian Persistence blog's team page and could change at any time.
The solution is to re-upload the image you want to be the og:image but make sure that its file name is alphabetically and numerically before any other images on the page. This is because the og:image selection works something like this: if you have two images IMG_1911.png and IMG_1916.png, the IMG_1911.png image will be chosen as the og:image because lexicographically IMG_1911.png is before IMG_1916.png.
If you want IMG_1916.png to become the og:image instead, re-upload it as IMG_1910.png, or with any file name that's lexicographically before IMG_1911.png. Then make sure to update the reference in the page/post to point to the new file. Publish your changes and then check the results with the Facebook debug tool.
This worked for me after trying many other strategies including changing image sizes, captions, order, CSS, etc. and I hope it will work for you. Let me know in the comments.