I think I'd be looking for a new therapist on this point alone...
. I told her I wasn't interested in going to church. Every session she brings up church and it's really frustrating.
If religion is part of how she practices, and not something you are interested in, then that's not going to be a good match for either of you.
I think this...
I texted her and told her that she doesn't know how close I am to killing myself and all she texted back was "if you're feeling that way please go to a hospital."
...is actually a reasonable response from her, especially given that the therapeutic relationship is still quite new, and she might not have enough information about you yet to feel able to safely assess the situation. Or she might not have had time to make a safe assessment of your needs. You reached out to her for support when suicidal, she pointed you in the direction she thought you needed to go in. It might not be what you wanted from her, but that doesn't make it the wrong action on her part.
It can be confusing sometimes I think when we read about different people's relationships with their therapists and the different levels of communication people have with their therapists outside of sessions, but your therapist gets to decide where she puts her boundaries and what level of support she feels able to provide outside of sessions. If you do choose to continue with her, this would be a good conversation to have with her. It would also be a good question if looking for a new therapist, to ask how they deal with clients needing support between sessions.
I have a good therapist that I've been seeing for several years, we mostly have no contact at all between sessions. If I was actively suicidal (which I think is what you are saying you were here?) and decided to reach out to her, I would still expect her to advise me similarly. Largely because actually she knows me well enough that if I'm contacting her between sessions then it must be really f*cking bad and I need a higher level of support in that moment. She might,
if she had the time to, offer to help me get that support (ie. Phone someone for me) if I was feeling unable to do that for myself.
That's not to say that she doesn't support me when I'm struggling with suicidality. We have talked about it often in sessions as it's part and parcel of life for me a lot of the time. But a crisis situation when she's not able to offer the level of help she thinks I need is a different matter I think.
This...
I texted her today and she said she was busy working and now she has stuff to do at home and sorry.
I think is an example of a therapist showing good boundaries. You texted her at a time she wasn't able to offer support. She let you know that. Again, if you do choose to continue with her it would be good to have the conversation about what level of communication between sessions is acceptable so you know better what to expect from her going forward.
I am sorry that you're feeling so alone with things and it doesn't sound like this is a good fit in other ways. How are you doing today?