I'm the same as you. Except for cats, animals generally make me uncomfortable, I'm not scared of most animals, they only exception is dogs. I was forced to be in contact with one of my grandparent's neighbour's dogs, which was a black lab. That worked fine, but I am still scared around dogs. Especially, since the next time, I saw the black lab and smelled me, he went crazy. Also, one of my grandparent's other neighbours, wanted me to meet their dog, who was very jumpy and excitable (not the best type of dog to get someone who is afraid of dogs to meet to try and get over their fear). She also kept insisting that I go up to her house and see the dog, over and over again at a party at my grandparent's place. I think she was a little bit drunk because she seemed to be forgetting that I already said that I didn't want to go to her place.
I am starting to resolve my fear around dogs on leashes, that aren't pulling on their leash, trying to get away from their owner. Dogs off-leash, are still a problem for the most part, unless the owner has good control over them or they are very well trained. I don't like it when owners just let the dogs wander around a public area, unless it's a dog park or something. A person who is scared of dogs, probably wouldn't want to hang out at a dog park.
On Friday, I had to go to the Palliative Care unit at the hospital. You are allowed to bring dogs in because the people in there are going to die soon and if they are with their pets, they may feel comfortable. I think some people just bring their dog there because they are allowed and they want to be with their dog though. This person, was living in the hospital, because their mom was in there and they weren't from the location where the hospital was. He brought his Russell Terrier dog and they just let it wander around the outside area. They weren't paying any attention to it. Most of my family was there when I was there and all the chairs at the front of the room were taken, so I had to sit in the chair closest to the outside. The dog LOVED people and couldn't understand that people may not want him around them, the dog ran inside, saw me and wanted me to play with him, I didn't know what he was going to do, so he made me nervous. Not to mention that I was more sensitive because I got up at 5:00 AM that morning.
Long post, I know, but, the it was kind of a long story.