Do you have any Razer software installed? Cortex, Chroma, anything like that could be an issue. If so, try uninstalling it.
If that doesn't help, or you don't have any Razer software, try using RivaTuner Statistics Server to manually limit in-game framerates, that is if you haven't already. It's a free download as well, at the bottom of this page:
https://www.guru3d.com/files-details/rtss-rivatuner-statistics-server-download.html
This is a helpful step anyway because your graphics card is fast enough to generate wildly high framerates and give itself an unnecessarily high workload in the process. But I'm also mentioning it because someone else with an AMD card reported what may be exactly the same issue a couple of weeks ago, and I'm not sure whether the solution was getting rid of their Razer software or limiting fps. Here's the thread, if you're curious; it also has instructions for using RTSS, in case that's helpful:
https://answers.ea.com/t5/Technical-Issues-PC/Screen-Blinks-Flickers-Black/td-p/11573013
The one time I tried using Adrenaline to limit framerates, it didn't work properly, but that was a full year ago. But if you want to try that first, the relevant setting would be "wait for vertical refresh." And if using that turns the game's UI purple, as it did for me, enable Custom Color, change the setting, and then revert the change and disable the feature; that fixed my issue when almost nothing else did.
As far as AVG is concerned, it's not usually a problem with Sims 3, but it's always possible the software is blocking some kinds of changes to the game's user folder. You can set exceptions for TS3.exe and Origin.exe (both if you have an Origin install) or TS3W.exe (with the W, disc or Steam install) as described in this guide. It was written for Sims 4, but the relevant settings are the same.
https://crinrict.com/blog/2020/10/add-exceptions-to-anti-virus-programs.html#avast
