If your Twitter account is locked because you have entered your password incorrectly too many times, this lock is only temporary. If you leave it for an hour the lock will be removed and you will be able to log in again - providing you can remember the password.
What to do if your Twitter account is still locked
If your account is locked for another reason, then you will need to access your email. You mentioned that you have recently changed the email linked to the account- have you checked both the old and the new email? Presuming the old one is still active?
I would advise checking your junk mail folders too, as sometimes emails can be filtered through to the junk mail folder.
If there is no email in your inbox or junk mail folder, then you will probably need to contact Twitter regarding the issue.
You can access the Twitter help centre here. It is really comprehensive, and has solutions for exactly this sort of issue.