Do you have any ability to pay out of pocket? Waiting lists to see psychiatric providers who take insurance (especially Medicaid) can be extremely long. If you are able to pay ~$100 you could see a psych nurse practitioner student through telehealth within a day or two who can evaluate your symptoms and severity and either prescribe medication or help you find a decent psychiatric ward. If so PM me and I can recommend a few services

You will not be hospitalized just for having occasional suicidal feelings/thoughts. Evaluation is more complicated than that. In most states you can only be involuntarily hospitalized if a provider feels that you are at serious risk of self-harm or suicide.

So it depends how often you feel this way, whether it's a desire to escape a tough situation vs. a true desire to die, how intense the feelings are, whether you have a history of acting impulsivity, any past self-harm or suicide attempts, whether you drink/use any substances, etc.

If you are at the point where you've started planning and thinking of methods and dates and notes to leave, then is best for you to be hospitalized. Better a short stay in the hospital, as scary as that sounds, than risking a suicide attempt which could traumatize your daughter and leave her without a parent forever.

If that does happen do you have any friend or family member she might stay with? If you choose to voluntarily self-admit you will likely be out within a week.

If you can't get in to see a provider the best way to do it IMO is drive yourself to a hospital with a psych ward and tell them you are thinking of killing yourself. Legally they can't just refuse to treat you if you, though if they're full they may transfer you to another facility. If you call 911 from home they will send an ambulance which will cost thousands of dollars for even a short ride.