"Is my personal information at risk of getting stolen?"
The short answer to that question is yes. The longer answer is that it depends on what was in the download, and what kind of information you store on your computer.
If you store any credit card information (and you should not do that) there is a possibility that it could have been captured. The same applies to any online banking information. Hopefully, you haven't saved any of that - or any passwords - on the machine, but as an immediate precaution you should change your email password and any online banking passwords.
Make sure your browser is set not to remember passwords, and not to auto-complete online forms.
The fact that you didn't give the software permission to make changes on your machine is good. Go into your downloads folder and delete the downloaded file. Then run a complete anti-virus and malware scan, and that should be an end to it.
Needless to say, you will never respond to any more pop-up messages on a web-site telling you that your computer's security is at risk.