H., hang in there, and good for you for continuing to search.
Here's what I heard in your note -
You did your research, listened to your son (he is communicating! Great! "Rat in a cage" is information, and more importantly, he is being responsible to listen to himself and to not lie to himself. He is also willing to tell you and himself how he feels. Many kids don't have that much maturity (or trust) - and so he can take an active role in his healing, as well as he is reaching out to you for help by communicating. You and he both can be thankful for (and even celebrate) that. Yes they blow hot and cold. That's why they are adolescents. Some have more challenges than others.
You have some key elements of health here that you and he need to be proud of since he is still working in trust with you and listening to himself, no matter how tough the challenge.
I would get a second opinion from someone who has successfully treated adolescent anger issues, preferrably from a referral from a friend who had success with that person, and then work with that new person only if you (and your son) are being heard and helped by the professional. (this applies to anyone, not just therapists) - A good one will allow you and your son to track his progress and include you, teach you what he/she is doing, and train you how to help, with respect and balance in the process. and a good one will remind you to be balanced and be sure to live your own life too so your son has a good role model and you stay in charge of the household and focused on where you are going with your life and your family's goals, not allow your son's challenges to rule by taking on a life of their own, but step out with your family mission and your own personal mission.
The diagnoses tend to smear a little from one label to another when dealing with related symptoms, and sometimes when there's more than one issue, which you may have - You might get several which have similar / same ways of treatment, so like others, please don't get too attached at trying to put "the label" on it.
If your heart tells you the label given by your current professional is simply wrong or incomplete, or the treatment isn't having results on all the signficant issues, that says there's a second professional opinion you need to get.
from what you say, don't be surprised if you find a few things mixed in in the diagnosis and treatment plan (they need to share this with you) - I suspect adolescence role confusion is one of them, and anger (plain old rage) compounded by frustration at failure to meet his own expectations, plus making sense of his confusing responsible experiences in the backdrop of his peers being irresponsible, may have some causes and solutions of PTSD, plus young males also have so few healthy role models so he may be getting out-of-proportion influence by peers and the media.
Many people working on a treatment keep a simple log of every day, write SHORT info on the therapist recommendations and then every day at the end of that day, briefly (no emotion in this, it's just a log, put your emotions elsewhere) note the worst adn best behaviors and your son's stated feelings (keep a separate one for yourself and your feelings) and breifly log any major events (or lack thereof) and be very careful to NOT let this log take on a life of it's own. It's just a list. you are keeping track of things which your memory may not remember well (like an allergy log but much easier and faster) - and then, when your therapist will tell you one thing (like, he's getting better in an area), you need to make sure you know if and WHY you agree or not to continue in that direction, based on recorded history, becaue you live in the results, not your therapist. It will also keep you accountable for your balanced behavior; it's very powerful for many reasons.
So - you betcha gal, listen to your heart, you have great courage, and I hope you seek out a recommended anger treatment specialist for a second opinion - there are funds from many sources if it takes extra money, you have a son who deserves a great life; he needs some understanding and some tools to help weathering his storm, and I am confident they are out there.
You have so much to be thankful for, and so does he for your commitment to him and your family. Make sure you stay aware of and make a little progress on your own life. Know that even just a little bit of focus on your vision of who you want to be (what kind of person) and what you want to do with your life, that will keep your adult balance when kids take a huge fraction of an adult's emotional resources. Keep doing what works best, and you'll get more of it. Hunt for a better approach if something isn't good enough. You'll do great!
Many blessings,
M.