Yes. If the content lives on your domain, i.e. the content can be reached at yourorganization.com or yourschool.edu, then you are responsible for the accessibility of that content. For this reason, it’s recommended to link to the third-party’s site directly for any content that isn’t accessible that you are unable to edit yourself.
Be sure to research any third party vendor you are working with and find out about their commitment to accessibility. Test their products and make sure the content meets your organization’s stated level of accessibility. If the vendor’s product does not meet your criteria, consider letting them know and ask if they are willing to make the adjustments. Many vendors are being pressured to update their applications or risk losing out on business, so many are willing to accommodate these requests.
Here is a good resource on working with the major social media platforms: Third Party Embeds | Accessibility Guidelines