I am fairly new to Android, but that's always cleaned up whatever issues I've had with ads (and those stupid Winner! pop ups). Not sure if that's what you are doing when you clear the history? Just in case, here are instructions:
Settings> Apps> Chrome> Storage
Tap on Manage Space, then tap Clear All Data at the bottom. Go back to Storage and tap Clear Cache.
EDIT: I just went and double checked that I had all the terms correct and forgot there are other options under Manage Space.
Clear All Data is kinda the nuke option, it deletes your bookmarks, too. If that's an issue, try the first two options under Manage Storage, first (unimportant storage (lol) and site storage). If that doesn't work, then you can go back and clear all data. I don't do bookmarks, so I just nuke everything when there is an issue.
Close everything out and then power your phone off for a minute. Turn your phone back on and hopefully that should do it.
It will log you out of everything you're logged into on Chrome, so be sure to have all your user names and passwords for forums and whatnot written down so you can log back in easily.
My husband uses CC Cleaner on his Android phone and likes it. That's all I know about it, though. Hopefully someone more Android-savvy will be along with advice.