Very hard to go from hands on response to dispatch, two totally different realms and yeah, I can see how that would make u feel helpless and heighten your anxiety. Keep track of when it hits you, write down your symptoms, the situation and use this "log" to help you recognize when it's happening. Keep a list of tension release exercises with you - stretches, deep breathing, shoulder shrugs, stuff like that, so u can do them when your anxiety gets triggered. Warm tea and drink it mindfully.
Also, think about it this way, on the "road" not everyone comes back alive, some we don't get to in time and some die, just the nature of the job, as we always used to say, "Sh*t happens, not your fault". Same rule applies in dispatch, you can't save them all and there is no blood on your hands that you don't unwittingly put there yourself because of your anxiety.
You're accepting blame that doesn't belong on you, it's simply an anxiety reaction. It spreads seeds of doubt in everything we do and every decision we make. This is why it's important to recognize when it's happening, accept it for what it is (just a body reaction to stress) and then work to return your body to a calmer state.
You are not solely responsible for these people. You can only do the amount your job allows. Go easier on yourself, none of what happens out there is your fault.
Wish I could've been there to "talk you down". Sorry you're having a rough go. Hugs.
Take care of you, you're number one.