Yeah, patience is so important right now, Mariposa. It's been my experience that online applications slow down the process. Three weeks seems like a long time, and it is when you are job hunting, but it might take a bit longer.
Stay strong with your recovery and things will work out. Fear and hopelessness are tough emotions to deal with, but you will be able to get through it if you remain sober.
I wish you the best of luck in your job search.