Only the first picture shows up

The widget will cache the results from Instagram for a short while which could be the issue. I recommend you install something like this:

https://www.ads-software.com/plugins/artiss-transient-cleaner/screenshots/

And clear your WordPress transients.

Ok it did the trick, I now have the latest image.

But is there a way to automate this, or prevent the plugin to cache the results ?

The cache will expire after a few hours. You can adjust the cache expiration time using the following snippet:

https://www.ads-software.com/plugins/wp-instagram-widget/faq/

Where do I put the snippet ? At the end of the php file ?

Try functions.php within your theme.

Ah it works now, thanks !!!