Can users see their own comment upvote number somewhere?
Unfortunately, there is no way programmed into StackExchange, that allows you to view your comment upvotes directly. However, you can still do it by using a MySQL query that I just wrote for this purpose.
- Go to your user profile on the site you wish to view comment upvotes:

In the search box on the right, you should see user:#####
. Copy this number (your UserID).
Go to https://data.stackexchange.com/math/revision/447134/568807/view-comments-sorted-by-score
At the very bottom of the page, there is a "Switch sites:" text box. In that box, type in the name of the site you wish to retrieve comments for. (The same site that you retrieved your UserID from.).
Tip: Clicking the little gear between "Switch sites:" and the text box allows you to switch between the meta site and the regular site.
In the "Userid" box (2 lines above), paste your UserID (which you got from your profile page), and click "Run Query" (next line).
After about 3 seconds, the list of your comments with non-zero score should show up.
- For the comment you wish to view in context, choose its PostId, and go to:
math.stackexchange.com/questions/[PostId goes here]
That will allow you to view the post with your comment that got a high score.