Edge is Microsoft's new Browser and is the default for Windows 10 along with Bing defaulting as the home page, which by the way controls your search history, and defaults to off, you need to turn in on with the Bing gear in the top right corner.
how would I tell if I am?
If you click the 3 dot ellipsis in the top right of the browser tool bar and you have an option to "Open with Internet Explorer" that would be a pretty good sign that you are using Edge. Heck..... if you even have a 3 dot ellipsis in the top right corner of the browser tool bar, I think that is indication enough.
My suggestion......
Click Start Button, scroll down to Windows Accessories and right click Internet Explorer, pin it to start and pin it to taskbar
and then use Default Programs in Control Panel to set it as your default browser, unless you prefer one of the many third party browser, in which case consider doing the same with one of them.
Edge currently, is just to edgy for me.