phone appeared infected and wouldn't let me do anything after webpage

No, it happened because you went to an infected web page, so don't go back to that page. And it didn't do any harm to your phone. You should probably also delete your web history and data, in Settings/Safari, as it may have left some cookies that could cause it to repeat.

Here are probably overkill instructions, but they won't hurt, either-->Dealing with Safari popups that won't… - Apple Community

I doubt very much that he couldn't turn off his phone, that was probably just not being aware of how to turn it off. But if any app displays a modal dialog it freezes that app until the user responds. And sometimes there is no way to respond to the dialog, especially if it's malware. If the app is a browser it is still possible to exit the browser, although going back to it will lock it up again unless the browser history is cleared. that's what I described in my first link--Dealing with Safari popups that won't… - Apple Community. The Google app is really just another browser.

Hi,

Although it sounds like nothing serious happened eventually, I recommend scan the iPhone for strange behavior. Also empty the cache/history of your browser.

Have a nice day!

[Edited by Moderator]

I STRONGLY recommend against installing ANY scanning software on an iOS device. Due to the way iOS works no app can do a meaningful scan. I suspect this post is just spam to promote the totally useless product.

Apparently I did something to offend you, sorry. Just trying to help.

No way I was trying to promote this app and spreading spam. So next time take it easy before you come to any conclusion. Thank you.

I'm surprised a webpage or any app installed from the AppStore could do something like that.

Do what? It can’t do anything. That was my point. At best it can slow down your phone while doing nothing useful.

He said that he couldn't turn off his phone. That was what I was referring to.