You're using the feature temporally backwards.
Now, I'm trying to call the API and find the change that I've made.
According to this page (Subscription Channels section), it seems like all changes will be found at /data/ChangeEvents, but the URL is not qualified, and there are no examples, so I don't know exactly where I should be directing the request.
Change Data Capture is intended for use with a subscription model. You, or your off-platform application, receive a stream of capture events that take place while you are subscribed and have an active connection to Change Data Capture. While you can use the replay capabilities of CDC to request the delivery of events that you missed while your subscription is offline, the intent is not that you should request change details on some cadence after the fact, and there's not an HTTP endpoint that you can hit to get a flat list of changes.
The Change Data Capture Developer Guide has code samples for how to subscribe using EMP Connector.
Your use case seems closer to the sObject Get Updated REST API endpoint.
