I agree with
@CaitMiller
This relationship seems very one sided to me. I think you're in danger of excusing his behavior due to PTSD. He may not be cheating (no commitment on either side) but he's not really being honest, either.
The guy looks to you for emotional support but gives nothing in return? Is this how you see a healthy relationship?
If you were THE ONE then he wouldn't be bouncing from you to her to you, would he? If he were all into you but PTSD was in the way, he'd be isolating from you and not "relationship bouncing".
I think you're a friend. Now with benefits. I think you very much want this to be more but you can't force these things.
You deserve an unattached man. (He is not.) You deserve a man who can support you, too. (He does not.)
I know you want to hear that he cares but it's PTSD getting in the way, but at the end of the day he's being deceptive and deception (lying/cheating/whatever) is always a choice.
I've read so many posts where people say PTSD doesn't make someone cheat. Follow that on down....cheating is deception and in your case there is no commitment hence no technical cheating but the animal is the same as he's being deceptive.
No, not PTSD. He's latched on to you for emotional support and is being deceptive in the process. IMHO.