You can get a list of your own measurements if you include a key - with sufficient permissions - that was created by you:
The key has to to have the "List your measurements" permission. The listing will return not only the measurements created with that key, but ALL measurements belonging to the user who created the given key.
https://atlas.ripe.net/api/v2/measurements/my/ also gives a listing of your measurements if you are logged in and will replace the ?mine=true query parameter.
Note that you can load multiple permissions on one key. You can read more about creating keys here.