MacOS High Sierra installed but not working

Hello,

I installed MacOS High Sierra on my iMac computer about a month ago, and since then a number of websites (of particular importance is my business's accounting site, Xero) have said "We don't support your browser Safari 9.1.3. Please update to a newer version or use a supported browser so Xero works correctly." However, when I go to update, it says I have already installed the newest version. How do I reinstall or update so I can get into the Xero dashboard.

Also, I have tried to update an Adobe program, and it is saying the update server is not responding?

Thank you,

Sarah