Rob: I’m not sure you really want to use Markdown for images. I love Markdown. Use it every day. But one of its weak points is images. This is mainly related to it being developed in 2003 when people were not thinking about responsive images.
If you know the size of each image, and if you know for sure that it will fit into the max width of your content container, then you could be okay. But most people don’t know this. Neither do I many times.
The alternative approach is to use a wee bit of HTML code. I don’t memorize HTML, but instead I use Typinator (or TextExpander or similar shortcut software) to put in this generic code:
<img src="fullURLhere" alt="textdescription" width="100%" />
I know this doesn’t answer your primary question, but your example is one spot where Markdown does not work great. That width at 100% bit is really important as it will auto-fit a larger image into the available content container. And of course you can set at something less than 100%.
As @instacks indicated it’s always possible to get a URL from Google Photos. It’s long, it’s ugly, buy copy/paste solves that pretty easily. An alternative that would probably be a little better is Flickr. But in this case only a little. The advantage is Flickr automatically creates multiple sizes of an image: so this might be helpful in some cases.
If the hobby page is for you, I still think the easiest method (with the shortest URL) will be to directly upload to your server area in a folder named “myimages” or similar. If this is for a client, then I completely understand why you don’t want to go that route.