Help! My new kitten is pooping and peeing uncontrollably!

I just got a kitten who is male, short haired, black, and 12 or 13 weeks old, not neutered yet.  He seems to be incontinent of bowel and bladder, although he may just not possess the instinct to seek privacy when eliminating.  A terrible person took him from his mother at too young an age.  He is letting single poops out (soft, slightly yellow tinge, but not diarrhea) and peeing anywhere and everywhere, even on humans.  He even wets himself during naps.  When kept in the bathroom with a bed, water, and litter box over night, I still found little poops around the floor. He allegedly had an anal/genital rash that was "almost resolved."  He was given a prescription for silver sulfadiazene for this, not sure why, since my understanding as a nurse for humans is that it's prophylactic, not a treatment for an existing condition.  His stomach seems to be slightly distended, although this could be a baby belly (do cats have that?) His gums ARE a little pale, but he's been eating and drinking fine.  His pee is usually clear with little to no odor.  I've been putting him in the litter box after every nap, play session, and after he eats or drinks.  No luck.  He's playful and happy, showing no signs of discomfort.  This problem has been occuring for 16 hours.  His anal gland is red and swollen, but this has lessened slightly since having a bath about 15 minutes ago.  He always seems to have a poop sitting right at the edge of his anal sphincter. Please help! Could this be an allergy to sulfa? His food? Anxiety?

PS: I have a vet appointment for 2 days from now, but I'm wondering if anyone else has had a similar experience and maybe I don't have to drop $200+ on the vet.

Does this kitten have a tail or is it tailless.

He has a tail

He needs to be seen by the vet immediately.

Can you move your vet appointment forward?  Give the office a call and see if they can squeeze you in asap.