Your description sounds exactly like how I once was.
Up until I was 20, I used to be terrified of dogs and would cross the street to avoid having to pass by them. My heart would race and I would start to panic just being in the vicinity of them.
For me, though, it was because I had never had any interactions with any dogs growing up. So it wasn't because I had been bitten or attacked or anything, I just didn't know what to expect. So I expected the worst!
What finally changed everything for me was my getting to know my best friend's dog, whom I had originally been so scared of that they had to lock him into the laundry room whenever I would visit. He was a Flat Coat Retriever (most harmless guy in the world!), but to me he was a scary ass big black dog!!
One day, he must have slipped out of the laundry room and halfway through dinner, I felt a soft warmth on top of my lap and when I looked down, he was giving me those big ol' puppy dog eyes and in that instant, I wanted to get to know him and give him a chance.
As I interacted more with him, and other friendly dogs, my fear lessened more and more.
Eventually (years later!), I actually wanted my own dog. Raising Huntley from puppyhood completely eradicated any traces of fear of dogs that I may have still had and completely turned me the other way, into a total dog lover! We're now onto our second dog.
The key is in understanding dogs, the signals that they give, and what to look for. Things like barking and stuff that may seem aggressive, but most of the time aren't. It changes everything when you know what you're seeing.
But I can still vividly remember what it was like to be gripped by that fear, and I always consider that when my dog is off leash and we encounter other people. I pretty much assume people are NOT going to be okay/comfortable around dogs instead of assuming that they will be. If I had come across off leash dogs on a trail, it would have petrified me back in the day, and I do not want to put someone else in that situation.
So my advice, if your fear was like mine (not triggered by any actual traumatic experience) then like others have suggested, try slowly interacting with calm friendly dogs of friends, in a calm controlled environment. Your life will be so much better for it! :)
you can always make more money but you can never make more time.
I think it's called work for a reason. Or else they probably would have called it fun-time at the fun factory.