Is psychic disease related to bad karma? I suffer from a psychic disease (borderline disease of personality) which has turned my life into hell for at least half of the time, I spend several hours a day crying desperately and nothing helps, not the psychotherapy nor the medicines. I am obsessed with the idea that I'm suffering so much because in some way I "deserve" it according to the karma law, for having done something very bad in a past life. Is it true? It may seem weird, but this answer means a lot to me. Thank you for your answers in advance.
In Buddhism, the teachings about kamma are for the purpose of promoting good behaviour rather than for diagnosing the cause of psychiatric illness.

Psychiatric illness is generally caused by a genetic neurological disorder of the brain or, otherwise, kamma (actions) in the present life, such as an accidental brain injury or intentional drug use. It is definitely not caused by actions in a past life. 

In his 2nd sermon about the ultimate truth or ultimately reality, the Buddha taught every component of the human life ('the five aggregates') can be subject to disease/damage (ābādhāya). 

Even the five aggregates of a fully enlightened person can have disease/damage (ābādhāya), such as the famous Thai monk named Ajahn Chah, who had a brain disease in his old age.

Therefore, about the cause of your illness, you should follow the advice of your doctor rather than listen to Buddhists who speculate superstitiously about unknowable past life karma.