Should I or shouldn't I. I see no reason why should I do It If I risk being put in mental facility. What do you think?
My advice would be, that if you are already speaking to him about suicidal thoughts, then he will already be providing the maximum level of care and treatment that he can. It won't improve the care you are getting from him.
If you tell him about an attempt to take your own life, he will be forced by law to act by reporting it. And a possible outcome is that you will have your personal freedom and rights taken away in a misplaced attempt to save your life.
Depending on your preferences, being subjected to this sort of treatment and this degree of loss of autonomy, may be less desirable than the freedom to take your own life.
If you understand this and it sounds like something that you would be in favor of, for instance if you believe that you do need forceful intervention to prevent you from attempting to take your own life, then I would definitely say go ahead and tell him.