Depression Support Group
Depression is a real and debilitating condition that is often misunderstood by family and friends. Its meaning can range from a prolonged period of sadness to an actual mental illness with specific symptoms. Find and share experiences with others who are going through the same struggles.
One thing for sure and that is if you discuss with your therapist about suicide in an emergency situation, your therapist is responsible to report you to a clinic and seek for immediate help. So if you must discuss this issue, you need to use PAST tense and also assure that the thought if suicide is fading not to post an immediate threat. You can bring it up as a prevention and need some support to learn how to deal with the situation better just in case.
If you don't have anyone to talk to and you're seriously considering it there are hotlines that I call when I'm at my end. They can even send a police officer trained for crisis to take you to the hospital to assess you if things get too much for you to handle. These services are nothing to be embarrassed about at all and have saved lives.
It's better to take advantage of these outlets than to worry about being "crazy."
Definitely keep your appointment and talk about what you need to talk about. If you don't threaten action, then you're not going to be hospitalized. Also, if you have mixed feelings about your family, going to see them could be aggravating the whole situation. Even better that you keep your appointment. Thoughts are just thoughts. Talk to your therapist about it, you will feel better... it doesn't sound like you could feel much worse right now, anyway.
When I was going through a time of suicidal thoughts all the time, I was sure to tell my therapist that I was not going to act on them, but I needed to talk about what was in my head. She was great about it. Didn't even suggest hospitalization, like it wasn't even on the horizon.
Good luck