Paranoia is a good thing when it comes to computing, both as a user and as a site owner/developer.
What you've experienced is called "scareware" these days, and yes, you should assume that some damage was done until you can prove to yourself otherwise. One of the first things these malicious "antimalware" programs do is to interfere with any existing AV software you may be running, so you may not be able to count on anything you have installed to clean things up for you.
You can try a trusted AV site to do an online scan (if you're running a Windows version, go to the
Rogue Security Software page at the Microsoft Security site). Just keep in mind that these things are often all but impossible to remove because part of the package is specifically designed to get around real AV software. It may not allow you to go to known AV real web pages, and may keep you from running known good antimalware programs (like MalwareBytes).
If part of the package was delivered and you're prevented from using AV to clean it up, you may have to resort to a system recovery, which is annoying -- but it's better than the alternative.