It actually seems more socially acceptable to say you don't like children.
@spriots I'm a huge animal lover who doesn't particularly like children (I don't dislike them, just not particularly fussed either), and I agree with you.
Having said that, animals are sort of objectified and commodified in our society in a way children (thankfully!) aren't. Animals are all around us. Certain animals become trendy in the zeitgeist (it seemed to be flamingos for a while, currently narwhals seem to be a big thing), and you can buy all sorts (notebooks, bedding, socks, mugs) displayed cutesy illustrations of said animals. A little fuzzy green owl is the mascot for the duolingo app (what do owls have to do with learning a language?). Capitalism profits from our love of animals and arguably pushes a deeper affection for them.
Therefore, perhaps one of the reasons people struggle so hard to accept a dislike of animals is because THEY'RE EVERYWHERE. It goes beyond a simple personal choice not to have pets, it's an exclamation that you don't like this very significant thing that seems to permeate our culture.
I'm not saying disliking animals is right or wrong. I understand why some people don't. I've known people who have feigned allergies just so others will accept them not wanting to play with their dog or stroke their cat, and I think it's ridiculous they have to do that.
As for OP, it does sound like rather an extreme aversion to animals, but unless it's causing a problem in your day to day life then it isn't really a problem. Your sensory issues may well be a trait of ND, in which case therapy (as some have suggested) wouldn't really help.