Just as the "virus" name says, mIRC is not a virus. Some anti-virus software will treat mIRC as if it were a virus because it can be considered riskware, which means that mIRC can be used to run malicious scripts (only if you decide to download and run a malicious/unknown script) and has in the past been used as a payload for some trojans.
From your post it seems clear you've intentionally downloaded and installed mIRC so it's clearly not a trojan, the only other question you need to ask yourself is whether you've run any mIRC scripts where you don't know exactly what they're doing. If you have, unload the relevant scripts from mIRC and delete them. If you haven't, just tell your AV software to make an exception for mIRC.
