If instagram.com is running, but you’re unable to access the website, try the following
If you are using a mobile device and the Chrome browser, tap the menu button (•••),
tap "History" section and click "Clear Browsing Data”. Now select "Cookies, Site Data" and click again on "Clear Browsing Data". This will clear your cached browser history and help you make a fresh start.
You can also try the browser’s "Incognito mode".
Just tap (•••) on the menu, select "Incognito mode" and you’re good to go! Don't forget that this mode doesn't save any login information and passwords: when you close the session no data will be cached or saved to your browser.