Married but filing seperately. Doing my master degree, paid for my own tuition, can I claim tax break?

No. Those filing Married  filing separately (MFS) are prohibited from claiming an education deduction or credit. 

When a married couple files separate, both of you automatically disqualify for quite a number of deductions and credits you would get if you filed a joint return. One of those things you lose out on is any and all education credits.