agneesze, were you registered on this site before the problem started? I wasn’t and also couldn’t log in here with my regular Twitter account.
Perhaps try creating a ‘throwaway’ Twitter account registered to a different email address like I did. See if it can access Settings->Widgets or not; my throwaway could when my regular couldn’t. My regular account started working two days later, which I assumed was the work of andypiper, but until he responds here we shouldn’t assume anything, especially because the problem isn’t fixed for everyone.