I think this is the type of thing you need, if you want to build the next Instagram or Flickr or Facebook:
https://piwigo.org/
Have a read of what it can do and look at some of the examples.
Download and install it on your web server. The install process is not much more different to Wordpress.
Theme it however you want, change the configuration in the settings panel or install extra extensions if needed.
It is open source software, and is therefore a free download for the self hosted version. So it falls well within your $100 budget.
Completely hackable. Build anything you want with it, if you have the time and skills needed.