This sort of thing does happen but I've never known it to happen like this...the only way you can prove your innocence is to prove that the computer had a virus on it that did what you say...if it's any consellation when I got a pop-up once that wouldn't pop-off for an antivirus programn I kept getting a pornography advert alongside it that wouldn't let up...the two must be related...I use malwarebyte's anti-malware to get the virus off my computer...Maybe if you got one of those logs of from scanning the computer with an antivirus then you can prove your innocence...I hope you can because it sounds like an awful thing to happen to someone...
Another thing could you possibly look into why the admin guy(Ithink you said) would set you up to get fired?...I mean if he's very knowledgeable about computers he could of actually put the virus on the hard drive or software e.t.c...in the first place.