That sounds fucked, dude. Best of luck with your complaint.
TBH now that you say this, it sounds like might be in a similar situation to me at my last job, which I persevered with for 3 years of riding burn-out (because the work was almost ideal for me, and the people were mostly amazing), and then quit.
There's already lots of other good suggestions here, but one point that might be worth noting: I think there are two different purposes types of therapy: psychological help (e.g. understanding your own brain, and figuring out ways to change it), and counselling (listening to your problems, and probably offering some professional guidance).
It sounds to me that given the circumstances you describe above, counselling is probably more immediately valuable - what you really need to do is to get some clear external perspective on your situation, from someone with whom you can share details privately. A good counsellor should be able to help you find multiple paths out of your predicament (you might also benefit from seeing multiple different counsellors, since they will all provide different perspectives). In my experience this really helps to ground your understanding, and helps answer the "Is it me, or them, or something else that's the problem?" question.
IF that process provides more indication that your angry outburst are because of what's going on in your head, and not just a fairly justified response to a shit situation, THEN maybe it's a good indication that you should look in to psychology or anger management approaches, or similar. If your angry outburst have existed prior to this work situation, then perhaps you could skip the counselling step, but it still might be worth it.
At my last job I was having angry reactive outbursts (which I had had in the past, but to a much lesser degree, and they were now spilling over onto family and friends), and getting anxiety (which had never happened before). I saw a few psychs and counsellors, and the last one I saw while at work said something like "If you anxiety is about a real work problem, and not an imagined/exaggerated/catastrophised problem, then it's not anxiety, it's stress". That really tripped a switch in my mind, and made the decision to quit super clear. Immediately after handing in my resignation my anxiety levels dropped off a cliff, and my anger slowly dropped back to tolerable levels over the following months.