I can't tell you what to do but here are a few things you might not have thought of, or a different perspective.
Your health is the most important thing ever. If you don't look after it then everything else falls to pieces. You can't give as much as you would like to your family, you can't do the things you enjoy, your happiness disappears. How much is a job worth compared to that?
I have yet to come across someone who has regreted telling their boss about mental health issues. It might cause problems in the short term, but as your health isn't affecting your ability to do your job then if you are good at what you do your helath issues will soon be forgotten.
With all due respect, you are not in the best position at the moment to assess how your boss will react. We all know that mental illness is accompanied by negative thoughts, low self esteem, low confidence, impaired ability to make decisions and think coherently etc. Your judgement is going to be biased because of this and your boss will almost certainly not react as badly as you think he will.
How important is the job? Do you love it so much that you can't imagine working anywhere else or are you afraid of change and moving on to a different place? What is the worst that happens in the unlikely event that you get passed over for promotion? It's only a job. You can find a better one if you feel that you need to, and get the promotion that way.
What exactly are you afraid of? Is it that people will know and look at you funny or treat you differently? Or are you afraid of the unknown? Your mind is in a horrible place at the moment, but it is a familiar place. Are you afraid of leaving the comfort of the known horrors for the fear of something that could be worse? If you don't confront change then you are never going to leave the horrible place you are now.
And maybe there will be some positives that come out of telling your boss. Maybe he will admit that actually he had similar issues a few years ago and admires you for telling him as he was too scared to tell his boss. Maybe he will offer you extra support and flexibility in your post to help you get through the worst patches. Maybe he will cover for you when you are receiving treatment by making up reasons why he needs you to run an errand for him that involves leaving site so that your colleagues don't suspect. Maybe he knows that there is a promotion coming up and he decides to put it on hold until you are in a better place to be able to apply for it.
I don't expect you to respond to anything I've said but I hope you will give it some thought