Do you have benefits with your job? There may be short-term disability benefits you can use for a couple months while you heal. It sounds like you just need rest — not necessarily institutionalization or sleep, rather time away from work to let you do healthy things like reconnecting with nature, exercising, frequent trips for therapy (weekly vs. monthly), etc.
Also, please remember mental health matters fall under ADA (which accounts for mental health among temporary or permanent disabilities) and Family Medical Leave (which would be unpaid unless your state requires the employer to accommodate paid leave). These are federal laws which protect you; your employer must provide reasonable accommodate or permit leave for a health condition without penalty. Talk to your doctor about this; he/she would likely provide documentation which your company would have to comply with. Then, maybe, you will feel more at ease about approaching work?
In the short term, if you need access to therapy but cannot find someone to talk to, ask about your company’s EAP which may be able to get you access to a therapist/counselor more quickly than if you investigated private practices on your own.
I really hope you are able to find a solution which helps you heal. They are out there. Don’t give up hope. Keep trying to find the one that works for you. Be patient and kind to yourself in the meantime.