Try going to Admin > User Management. If you're able to change permissions of yourself and other users, you likely have admin access. If you don't have that option, or are unable to change anything, you probably don't. If that's the case, you can work with someone in your organization who does have admin permissions and make sure you're able to create a calculated metric.
I'm unfamiliar with the HOTE distribution list, but if you've already arranged to have that as your point of contact, I'm not going to say otherwise. Adobe standard support email is email@example.com, though. Since they aren't allowed to touch permissions, they'll likely have you go to an admin in your organization anyway.
I think I don't have admin privileges (how can I check this?). I have already written to firstname.lastname@example.org on last Wednesday about the issue I am facing, but did not get any response yet. How long do they usually take to respond?
While logged into adobe analytics, I am able to go to Components> calculated metrics.