I freaked out when I was getting an MRI on my brain and had to leave b/c I was claustrophobic. Will an open MRI be much better?

Will help, but . Clarity and precision of image a bit less accurate than closed mri, but far less problem with claustrophobia. Might also consider "stand-up" mri.
Better. An open MRI will be less enclosed and generally better tolerated. You can also discuss trying an anti-anxiety medication with your physician.