Hello Ajeya,
If you are able to see the communication channel in the CC Monitoring then you should be able to see it in ID also, as the configuration for the channel is done in ID.
I am not sure why you are not able to see the channel there.
Still, click on the channel in CC monitoring and see the service associated with it.
Check for the service in the ID and then you will find the channel enlisted under it.
Thanks,
Kalyan