Thank you for trusting JustAnswer with your important question.
You have a lot going on, and the lack of sleep can be from more than one source (anxiety, mania, triggered parts who don't want to allow sleep because they are afraid of nightmares
/memories, and burned out adrenal glands from all the stress
!). Seeing your doctor to rule out any other medical issues (like hormones, and thyroid) and to check your body to make sure this serious lack of sleep isn't causing physical damage (increased heart rate, increased blood pressure, changes in organ function like kidney and liver tests) are worth considering.
You may need a different medication to help you sleep. Ability and Seroquel are both used to treat mania, and I have seen both used to help with sleep disturbance (most commonly is Seroquel, which I've seen used for racing thoughts, nighttime anxiety, and even treatment resistant depression that can disrupt sleep). The Ambien may not be targeting the right brain chemicals to help you get your body to go to sleep.
As far as the cutting, your therapist has a legal and ethical obligation to keep you from being a harm to yourself or others. When we work with a client with self-injury habits, we look for potential lethality, increased suicidal ideation, and increased severity of impairment (lack of sleep, overwhelming depression, unbearable anxiety, feelings of hopeless or helpless, etc) to help judge when inpatient treatment may be needed. If you are willing to try medications, and try to reduce your self-injury tendencies, your therapist will probably not have to force you inpatient. But if they fear that you no longer have the emotional resources, medication compliance, or external support system to stay safe from potentially lethal self-injury, then they may attempt to force you to go to a hospital for observation (23-72 hours depending on your state laws and severity of symptoms).
Talk to your therapist about your concerns, and what kind of contract you can make with her to avoid inpatient treatment so you know exactly what her boundaries are and exactly what would make her attempt an admittance for observation or treatment. She may ethically and legally just want the security of having you see another professional who also deems you safe enough not to need hospitalization. And she may want you to try medication to help therapy be more productive. It's hard to do therapy when you are manic, sleep deprived, or otherwise in an extended mental and physical crisis.