it sounds like you need more support and should be honest.
if you are wondering if you should be honest, your inpatient situation must not be that bad.
also, it sounds like you are suicidal but also ambivalent, since you are considering discussing things with a doctor
actually going through with suicide takes tremendous intent because of survival instinct (SI). To really end things, you usually have to be really intent and set on doing it. you probably lack that intensity of desire to end your life and won't commit suicide soon, so you should keep trying to live and get more help
a lot of people here have made plans to die, either don't go through with it or botch the attempt, and end up worse because they didn't plan they would be alive. you should plan to be alive.