Sorry to hear about the post-combat issues, sounds like you're doing pretty good though.
The PTSD should not be a problem I would think, since it doesn't manifest in a manner which might interfere with flight operations.
Clinical depression would be disqualifying until it is resolved. In the past, all psychiatric medications were disqualifying but you could get cleared after being off the meds for six months or so (and the underlying condition resolved). A recent rule change now allows people to fly while taking certain meds for depression, but the underlying condition has to be controlled.
Sounds like you are OK now as far as depression and meds go. Be advised that airlines may have higher standards than the FAA for new hires, but I think most US airlines will be OK if you are off meds and doing fine.
The TBI might be more complicated...the FA will be concerned with it's affect on your psychological health and mental acuity (memory, reaction times, etc). If it was mild and you have no measureable symptoms I suspect they will give you a medical after some evaluation but I cannot say for sure.
For these issue you really should get help from an aviation medical consultant...if you just go to an AME he may not be particularly helpful. A consultant can advise you on your chances and help you prepare your medical record and FAA medical form. They can also walk you through any required specialist consultations (which I'm sure you will have to do). There are several companies that do this, Virtual Flight Surgeons is one (google).
Also be advised that after all is said and done you will want to have a clean first class medical without any waivers or restrictions (except corrective lenses are OK). You might have to fight them on that, depending.
Also note that the FAA has recently compared records with other federal agencies to find pilots who had FAA medicals but were also claiming disability (which they did not report to the FAA). Some of those pilots are in jail now, so I would be very, very reluctant to lie about anything which the government already knows (ie military medical history). In the past, different agencies never shared notes but now that everything is computerized...
Best of luck with this.