Suicidal thoughts are pretty scary for a lot of people, including professionals--particularly those who do not specialize in mental illness. I think that you might find that a therapist will be less freaked out by it than a general practitioner. And in reality, what your doctor did was get a second opinion (with the social worker). She wanted to error on the side of keeping you safe.

I'm sorry it was so scary for you though to go to someone and ask for help and have you feel threatened like that. The system isn't meant to work that way. Frankly if everyone who had occasional suicidal thoughts was put into a hospital, there would be no beds left. And if it is true that you just want the pain to stop, but not actually die, then I think there's a good chance you would be really helped by outpatient therapy. I hope you will take the risk of asking for help again.