I'm sorry you are having such a rough time. I can relate. I have been there many times. I actually have a plan even now, but no intent (the depression has lifted some). I think it may be good to talk to your T about your plans. Confidentiality rules differ by location, but many times T's will talk more about it before they jump into action (unless you are telling them you will kill yourself as soon as you walk out the door). If you do have a plan with means and intent to carry it out, your T will likely encourage you to go to the ER, or send you if you refuse.
I know it's scary, but trust can be a good thing. It could mean that he is someone you think may be able to help you through the dark times. You must be hurting an awful lot to be considering suicide, but he can't help you through it if you don't tell him the extent of what is going on. If you are on meds, it might be time for a med tweak. If not, then it may be time to put a crisis plan together. Like I said, I pretty much always have a plan in place (kinda like an "escape clause"). I have learned that when the intent gets too strong, I need to reach out. My T and I will talk about it and she will assess my risk. Generally, it's really helpful for me to be admitting to that level of hurt. We talk about the things that are making me feel so hopeless. A lot of the time, talking about it and admitting how bad things feel helps lessen the pain of it. It doesn't take it away, but it gives me a new perspective on it.
(hugs) I hope you can be ok trusting him and opening up. It's a huge risk, but it may totally be worth it. Not everyone breaks your trust. Sometimes even when they do in one moment, it's for the better in the long run. Good luck and please reach out to someone if things get too bad (and before you make an attempt)