I note that we can follow the up-/downvotes on our questions and answers, but there is not a convenient place to find stats on the upvotes on our comments on questions and answers. Is this one of the advanced privileges earned after attaining >10,000 reputation or some other qualifying event?
There's very little that you can say about comments. This is by design: comments are explicitly relegated to a second-class, transient role, and SE has been very clear that anything that would increase their importance (thereby turning SE into a discussion-board type of forum, at the detriment of the straightforward readability of the Q&A format) will not be taken up.
This Data Explorer query can find all your comments, including their score, but that's about all the information available. There is no rep-earnable site privilege that enables any additional visibility into the comment statistics.
This is another way in which the decision to have comments be second class citizens shows in the interface: there is no feature for tracking such things.
You can construct a query in the Stack Exchange Data Explorer to learn about the situation up to the most recent capture.