Limeapple, hello!
I read all your post. I sometimes found trouble to understand humor sense in the jokes you described, but it’s not your fault. 😀

Keep calm, what Mammu says has lot of sense. Have you seen the Big Bang theory series? It’s awesome how they all have a place in the group and how over over differences, there’s always their friendship.
Rory was a bit rude but honest. I’m sure it wasn’t an attack. He was only expressing why he can’t reply. A long text from a friend needs time to be read and he probably didn’t want to reply whatever without reading with time. Nonetheless, you already know he likes short texts.

It’s normal you question any detail. I used to do it all the time and still I do it although not so often.

While you are able to see your psych again and a though like that, a doubt pops up, try in private to see the whole Rory or the whole Kate. I don’t remember the other friend’s name. And question yourself what that person have done in other occasions that
could contradict the one you felt rejected or bothered by.
Another strategy is what it has been said acceptance of differences.
Take time to (not ruminate) but to have a time where you accept something made by others hurt you, without dwelling on. I usually do this with meditation. It helps to pass the page. Not sure if I explained this point very well.
Have you worked mindfulness with your psych?