On Firefox, you could try the following: go to Settings - Privacy & Security (or type about:preferences#privacy
in the URL bar), scroll down to Cookies and Site Data, click Clear Data..., click Clear and restart Firefox. If you want to play it safe, untick the Cookies and Site Data item before you click Clear, but if that doesn't help, you'll have to try again with both items selected -- this means you might have to log in again on some sites.
All this does is delete cached data and other temporary files, which if I understand Vekseid's diagnosis correctly, is what's giving you trouble. I'm sure other browsers offer a similar functionality, I just don't use those myself.