I had to really think about how to answer this... given it's something I always had (and for a long time assumed everyone was the same way), but didn't really know it or accept it with confidence until I was about 30 or so. Not that I didn't have inclinations or thoughts, but self doubt played a large role and when you're tapping into the emotions and fears of others... they don't necessarily validate what you're picking up on. More often than not, they'll deny, discredit, say you're crazy, etc etc. It's not comforting to realize that someone can see through you and invade your privacy so to speak. I didn't have anyone to help me so there was A LOT of trial and error.
Funny you should mention military because I was raised by men- all with military and/or firefighter & first responder background and jobs. As you can imagine, there wasn't a lot of room for being 'sensitive'. I was raised with a 'deal with it- don't be so sensitive- walk it off- tough it out' kind of mentality. This crippled me just as much as it helped me. It crippled me in the sense that those kinds of abilities and experiences 'don't exist' in that world- hence, my self doubt. Yet, as I got older- it helped me enormously as far as giving me the skills and mindset to deal with it in a very practical and logical way.
My father used to worry because I spent so much time alone and preferred being around animals. Not that I didn't have friends, I had quite a few, but I was much more comfortable being alone (or with just one friend rather than groups) with books and animals. Animals' emotions are clear and pure, easy to deal with and be around. People are more complex and when I was young (and looking back now) I couldn't differentiate between my emotions and those of other people.
When I first read your question, it caught me off guard because it's been more of a journey than any specific moment or event- so I had to think. The first thing that came to mind was a memory that I am truly LOATHE to admit and frankly, gives me some trepidation to 'put out there', but it's the truth. Bear in mind this is a memory from when I was about 4 yrs old (I have a very long memory). I know I was about 4 because I hadn't started kindergarten yet, I didn't start kindergarten until I was 5. So, I guess I could've been anywhere from 3 to 4. Anyway, here it goes....
I was at my babysitter's house where my dad used to drop me off before he went to work. My brother was already in school. There was a boy, a toddler of about 9 mo/1yr or so, couldn't speak yet... and to this day I remember his name, Ben. He was in one of those toddler walkers that was a circle with the seat in the middle and wheels all around it and a little shelf that went all the way around him, like a donut. I don't know what they are called, but he used to push himself around in it. He was always smiling and happy and everyone just doted on him when he was there- the other parents, the babysitter, other older kids that were my age and older. I got jealous of all the attention he was getting and one day when no one was looking, I pushed him down a step that went from the kitchen to the living room. He went close to the edge and was looking over and I just pushed him. His walker on wheels went over with him in it and he was crying. I immediately started crying, feeling his fear, his terror- as he was feeling it. He wasn't really hurt (thank god!), but he was crying from the fear. To him, it seemed like a very long fall. It wasn't like a normal empathic response where you see someone has a broken arm and you had a broken arm or were hurt once, so you can empathize, remembering what it's like to be in that pain too. I literally felt his emotion, his fear, his terror and I was crying as much as he was, if not more. I also felt incredibly guilty after I did it, I actually felt what I did to him. What's worse is, my babysitter came running over and thought I was trying to help him- which by the time she got there, I was. By the time she got there, I was holding him and hugging him, crying and saying I was sorry. He calmed down and smiled at me. I doubt very much that he even knew that I was the one that pushed him, no one did. After that, I became his protector and de facto big sister. I loved him and felt his love for me and was ashamed I could've ever caused him any kind of pain, emotional or otherwise. I am still ashamed of that incident, but in my defense I was only 3 or 4 yrs old at the time.
Obviously, I wasn't cognizant of it then but looking back, I think that was probably the moment. There've been a lot of experiences and incidents since that time, where I was cognizant and 'coming into my own' so to speak, experiences where I've helped people more than I realized at the time, but found out later (sometimes years later) when they told me and thanked me; but that memory and those emotions from that one experience when I was 4 are as clear to me today as they were when it actually happened.
I'd be very interested to hear about what the military therapist has told you and to hear about your experiences. What's the difference between a military therapist and a non-military therapist? I'm curious to know what led her to tell you that and what led you to her. It's a strange thing to realize way into adulthood that 'Oh! Not everyone experiences this!' For the majority of my life, I assumed everyone experienced things this way and that I just had a harder time dealing with it.