Can a person who hacked your fb account go into your bank account?

I wouldn't have thought so but if you have a bank account that you've associated with Facebook, then may be able to buy stuff and send it to themselves.

yes your cellular phone text messages might be linked to facebook messenger which can be used to receive authorization codes to log in to your online bank account.

change your facebook password to a strong, unique password. don't re-use passwords between services and sites. don't use your browser's password saving feature, and don't use apps such as "Lastpass" that are intended to help you save your password in a convenient way.