Check your network connectivity - if you're using mobile data, switch to Wifi or vice-versa. Check also if your Instagram app is up to date.
Try clearing Instagram's cache by going to Settings > Apps > Instagram > Storage > Clear cache. If the issue persists, restart your phone.
In case Instagram still doesn't work, try reinstalling the app.
You can also check if your account is still accessible by visiting the Instagram website. If you can't access your account either, it may be possible that Instagram is experiencing an outage. Log out and try logging in after a few hours.
If you can access your account settings, report this to Instagram by going to Menu (3 horizontal bars) > Settings and privacy > More info and support > Help > Report a problem (or Menu > Report a problem from the website).