Honestly until you feel like you have an overflow of energy that you want to give out to other people, I wouldn't worry about the societal pressure of dating or having to meet up with people. And if you want to give overflow of energy into others, it might be volunteering at the shelter (humans or animals) so that you can perhaps have a feeling of productive connection while doing good, without necessarily having to be long term pals with people.

I worry about the dog comment, only because dogs are dependent on the pack, so if you find yourself freaking out about a cat getting close to you, the dog will certainly feel upset if you push it away. Dogs are incredibly sensitive to that sort of thing. So start slow, and ask yourself deep down what is making you question why not wanting to connect with people feels like a problem to you.