Constant “Database Update Required” messages

Hi, we recently updated our site to Word Press version 4.7.4. I was told we could only go this high because of our server’s PHP limit.

Now, any time I try to access anything from the dashboard options, I keep getting “Database Update Required” prompts, and then I click “Update WordPress Database”. After that, I get another prompt that says “No Update Required”, and then I click “Continue”.

Is anyone familiar with this? These prompts happen a lot, and intermittently. Sometimes, after clicking “Continue”, I get re-directed to our site’s home page instead of the page I was trying to access.