Hi, I'm so sorry you are struggling. Do you have anyone else you can talk too? Like a family member or friend? I'm glad you told your therapist and I'm sure that she cares, even if it doesn't feel like it. I, personally, would go to the ER or hospital. Even if you would never do it, you should still get the help you need. I have dealt with suicidal thoughts a lot lately too and I would never do it. But my therapist almost put me inpatient until I promised I would never do it. I think you should at least get a different therapist if you feel that she doesn't care. Going to the hospital is up to you, and if you think it's necessary, then I'd go. Better safe than sorry.

BTW, I'm not very good in giving advise, so I apologize if this didn't help. :(

I wouldn't go to the hospital unless you are planning on doing it. It's not a very good place to be and has always made me worse...

If your therapist doesn't care and isn't doing anything to help I would try switching therapists

It seems that you have just the awful thought of wanting to die but there is something that is keeping from doing it. keep fighting. Call crisis hotline talk to someone about your thoughts... maybe what is bugging you or causing you to think this way..
If you think your in danger go into hospital its better safe then sorry.. maybe you just need to talk to someone and can leave with a better frame of mind... or maybe you need to stay in a safe place for the night... and you can leave when you are ready and are feeling better. This might help. They are not going to commit you unless your a danger to yourself.. meaning thinking of ending ones life does not mean your at risk... now saying your going to kill yourself and having a plan and the means of doing so, yes they will commit you then... There is a difference... so know that, as many have that in their mind that if you go to the hospital thinking about those awful feelings that they are going to keep you, thats not the case they have to by law have reason to keep you, which would be to keep you from harming yourself.. but thoughts and for sure going to plan to are two different things. Mental health is more known and dealt with different from before, so know this.. So if you need to please go to hospital if you are not to that point then call a friend, talk it out... or talk to crisis hotline that helps... or sometimes just keep busy... really busy gets your mind of the topic and thoughts... go for a run... workout... do something you love to do.. anything to get your mind off the topic... I know its not a fun feeling...scary really when you have no intent and are thinking of different ways that you could end your life.. I was there not too long ago... I had a few bad days and I tried to over and over push down the bad days but it only got worse.. to a point where I was walking around and everything I came across... I was thinking of how I could end my life, yet I had no intent to do it.. I had to go into the hospital and I talked to the nurse and after left with a better mind.. I just needed a good vent..
Hope your feeling goes away.. take care, and if you need to talk message me.
hugs