Malware and virus links

I was on the same site in the google chrome app for iPhone, and then started redirecting to a lot of different sites. Then it brought me to a site (I don't remember exactly which one, but typical enough for advertising). I managed to notice which sites it goes through and checked them. Some of them were suspicious.

The strangest thing is that after pressing the back and forward button, a “download” button appeared at the bottom. It was written download and some strange file name. I don't remember the details, but I clicked “no”. Now I doubt it was a message from Google or an iPhone at all. Maybe it was a phishing message on the site itself that brought a virus to my phone. After that, I checked the downloads in the app and there was nothing.

Actually, it was all in private section. I immediately cleared the history of Safari(as it was nothing about Google chrome app) in settings. Also, I deleted the app and restarted my Phone.

What else can I do? Is there a chance that a virus was downloaded (especially considering that I clicked something on a suspicious website)?