The simplest way to update Internet Explorer is to run the browser, then press the small gear like icon from the upper-right corner of the window and click the About Internet Explorer button.
The window that opens up shows you the current version of Internet Explorer, so you can see whether the update was installed or not. Additionally, the same window also has a small box marked as Install new versions automatically. If you check that box, Internet Explorer will be automatically updated as soon a new version is pushed by Microsoft.
As far as the SI alert, it could very well be just a glitch. I recommend manually checking the version as described earlier and you will be able to tell.
If there's actually a problem and the update isn't installing, make sure that you have administrator privileges on your Windows before running the downloaded file and that you don't have an application like DeepFreeze on your PC as it automatically uninstalls every new thing that you install each time you reboot your system.