If you are on a Mac, a good alternative that I recommend for this use case is Flotato. I run a calorie tracker web app and as you said, it is so much better to isolate a specific app from the browser. The added advantage is that Flotato runs the Safari engine, so you don’t get the battery drain from a Chrome instance.
I’m sorry Zvi, but I’ve now realized that you are running on a wordpress.com subdomain. You won’t be able to use Cloudflare, unless you upgrade to the Wordpress business plan (£20 a month) so that you can install plugins.
I don’t have any simple and effective ideas for what you could do, other than putting a call to action for somebody who has more Wordpress experience to help you migrate to a more sustainable setup.
I checked and all the images are hosted on googleusercontent.com which is a subdomain that Google uses to hold third party content. The images are probably getting rate limited, as the system serving them was designed to prioritize Google content and not user generated. The practice is usually called hotlinking and that’s why the server started to rate limit. I recommend that you try and host the images on your own Wordpress. Otherwise, maybe throwing Cloudflare in front of your site as a caching layer might be an easier solution.
(Disclaimer: I work for Google as an engineer, but I’m very far away from this system.)