There's no way for us users to check our report logs as it's a different system from the tickets.
However, you may PM a moderator for a confirmation. Provide the needed information (link to the arena and the comment being reported) and wait for their response. It's best to ask them right away since we can't tell if your reports are going through. If they are, then you'd just be flooding the queues with multiple reports and is considered spamming and abuse use of the report system. Notifying them about this matter should excuse you just in case it did really went through.