I hope you'll take some time, first, to give your therapist a chance to help you and/or to talk here about your fears and concerns, and second, to spend some time researching here before you decide what your methods are. Don't worry, you don't have to choose a method to be accepted here. The only thing that unites everyone is being pro-choice, and that choice can include one deciding to live equally as well as to ctb. No one will rush you to make any kind of decisions, but especially not to ctb. If they do, report it to a mod. It's not a pro-death site.
I noticed you've just joined, and someone mentioned SN to you yesterday, but there is a lot of material to read about it, as well as success and failure stories to consider, before you can reasonably become certain it's the right method for you should you choose to ctb. Also, if you use the site search for bleeding out, you'll see it's been discussed a lot on the forum and is an extremely difficult method that often fails because of coagulation. It's not at all like the movies.
About your therapist. In general, they're difficult to talk to about ctb because some countries' laws require that they report suicidality, and many (but not all) folks have had bad experiences with psychiatric hospitalization. So if you haven't brought it up to him/her before, it's good to ask her/him what is okay to talk about with them. Often it's safe to talk about suicidal ideation as long as one does not have a plan and is not currently planning to self-harm. In general, therapists are not pro-choice,but s/he can perhaps give you coping tools, or help you figure out and work through the root issues for considering ctb as an option, or why you believe you're a bad person and why you believe you deserve to die.