Luckily I do not have allergies. But yes, I believe there is a difference between long/medium and short haired cats. The allergies come from the dander in the fur so the longer the hair the more dander (I'm guessing on this, I'm not an expert. But it sounds right, LOL) or the more difficult it is for the cat to groom it out on their own.
My cats are short haired. I lived with a roommate years ago with Taz and she was allergic to her moms and sisters cats but Taz and I lived with her for over a year and she was fine. He even slept on her headboard at night and she had no problems. Bruce's brother is allergic to his other brothers cats (one is medium hair), but he isn't as bad when he's here.
We have plenty of long haired kitties here on PT, perhaps those will see this and weigh in.
I say give it a try. You will know if it's not going to work within two weeks, as this last kitten showed you. You'll never know if you don't try.