You don't have to install Instagram's app to create stories on your phone. The photo-centric social network is adding support for posting stories directly from your browser. You have to be content with still photos and text overlays (no video or clever filters here), but this gives you a way to join in the action when you don't have room for the app or just don't care to use it.
Also, the Pinterest-like ability to save posts is coming to your phone's browser. If there's a travel destination or savory meal you want to remember for late, you can bookmark posts and visit all your saved examples.
These features will take a few weeks to reach everyone, so don't be disheartened if they aren't available right away. When they do, though, the mobile web version of Instagram will be considerably closer to its native app version. There are still clear reasons to download the app if you can (receiving notifications and posting video in particular), but there isn't as much of a rush as there was in the past.