If even if you went inpatient, it isn't locking you up. You're right that it's an irrational fear - and you're already working through it!

And another fairly logical conclusion to help: don't try to kill yourself. If you don't attempt it, then you can't fail, and thus can't have a hospital show concern for your wellbeing. Thinking "then I have to make sure to do it right" is less logical than not attempting, because there's ALWAYS some chance that you'll survive and paralyze yourself or something. And there's the added benefit of always having something to stop you from trying! It's a win/win!