I have just gotten back on a bike after 36 years of not biking at all (I'm 52). I was lucky in that I did pretty well getting back to it with a short practice period, but I certainly understand your fears and frustrations. I experienced all your same shakiness and self doubt.

I took a borrowed bike to the big high school parking lot after dinner but before dusk, and being summer evening there were no people, parked cars, or traffic to speak of.
I went several days in a row just to practice getting my balance back, doing wobbly circles, zig-zagging, braking, getting on and off, etc. Each day was it's own mix of success and frustrations, but by the end of the week I could see I had in fact improved.
Be kind to yourself! Look at it as something you are doing wonderful for yourself rather than it a stumbling block or a failure to be dreaded. It's a learning curve. Think of it as the worst part being behind you now, just like when you started changing your habits to lose weight. The worst part is over with- you will only get better! You will be slightly more skilled at avoiding a fall now that you've had your first spill.
Do these little practices for only 15-30 minutes unless you WANT to make them longer because you are having fun. Make SMALL goals that are easier to achieve. You'll see real results after another few practice sessions. Don't give up- your biking will become a joy and a freedom in your life!