Your request got turned down? In that case I would ask when it could be scheduled. He has to approve the request for some time off or you need to discuss that with HR. (I am presuming that you actually have the time available to take.) Your vacation is part of your compensation, you are entitled to it, but the manager has some say in the scheduling of the time. If he refuses to schedule the time, then HR will need to deal with it.
If you get a scheduled time, that can relieve some of the pressure and anxiety. It is easier to hold on til Sept 5 than it is to hold on forever. Since you have depression, if you see a therapist, I would strongly suggest that you discuss short-term ideas for how to hang on until the scheduled vacation.
Some things I can think of involve making sure you get enough sleep, taking some time for yourself outside of work to do fun things, and meditation. I have found that a five minute meditation where I first relax through deep breathing and then tell myself to release any anxiety stored in my body really helps. Exercise is often helpful for depression. Remember when things that stressful at work, a five minute break in the rest room can help.
If you go to HR, take medical documentation that you need the vacation in case their response dictates that you need to up the ante. Go with a plan for who could cover your job while you are out.
If you need to provide medical details to HR, specifically request that they not share any medical details with your supervisor since he has used such against you in the past. Give them details and dates of those incidents. Be prepared with all this before you go to HR.
When you approach HR about this, you want to appear as the professional who is making a request that was unreasonably turned down and show that you tried multiple times to get a vacation approved and that he would not approve one for any dates. You want to appear as the reasonable one in the conversation. It can help if you talk to your state Labor department and see if there is any labor law surrounding vacation time. The more organized, knowledgeable, and professional you appear, the more they will take you seriously as someone who might sue the organization if they don't do the right thing.
I would also ask that you see if HR can arrange for you to be transferred to another boss since this one is hostile depending on if there is somewhere else you could be working.
Note that going to HR can be a career limiting move at that particular employer. Do it if you must to get the vacation, but consider that you need to continue working there and the supervisor will not be happy (of course he already is not happy so that is less risky). It might be time to start a job search for something else. It might even be a better choice in your circumstances if you can apply for a transfer without bring up the whole vacation thing. Just getting away from this boss will likely reduce your anxiety and you can tell your new boss a few weeks after you start that you have x amount of days to take before the end of the year and when would be a good time to take them.