Your question is impossible to answer without have direct access to your install so all I can provide are troubleshooting steps I would take.
I'd start by contacting your web host to see if they are having issues on their servers or have changed anything on the server. A change/issue on their end would explain the sudden sluggishness if nothing in the actual install changed. The error is happening because the script can't execute within the set 90 seconds. You can increase the value in your php setting but I doubt that will fix your sluggishness. The error is a result of the sluggishness, not the cause.
I'd also take a look at your PHP error logs to see if anything obvious is showing up.
Another thing to check is the speed of you EE control panel... in the footer you will see the execution time for the page... eg: Script executed in 0.4833 seconds. If the CP is speedy but the front-end is slow, you should start looking at things that affect the front-end only. If the CP is also slow, the cause is most likely not anything related to EE and your web host is the person to call.
Also check the Network tab in your browser's dev tools to see exactly what is slow? Is it the initial GET request? downloading of external JS?
What does running a tracert show? Any network issues between you and the server?