Hi Nina123,
feeling burned out and depressed is common for people who arrive here . For the situation to improve - whether you separate or not - it is critical that you exercise sufficient self care. Moving out - possibly temporarily - can be a positive step (in the LESSON 6 there is a link to therapeutic separation workshop).
BPD is very complex condition and predictions are impossible. However statistics show that it is a condition where targeted therapy can make a difference and symptoms can often be reduced on a level that they don't fit the original diagnosis anymore. So yes, it is treatable but treatment requires some level of buy-in to learn more constructive coping strategies in DBT by the pwBPD.

,
a0