@nprofile1q... Twitter by default doesn't log you out when you get suspended, so try logging out of all your accounts. If that doesn't work, try clearing the cache (never tried it myself). And if that doesn't work, try making your new profile on mobile.

From what I experienced, twitter doesn't accept any mail service other than Gmail, and you have to provide a phone number, too. For phone specifically, there are websites that provide you with phone numbers for SMS.