He obviously already had bladder/urinary track inflamation since that is why you took him to the vet in the first place. The catheterization was to try to remove existing blockage and the antibiotics to fight infection. FUS is just a catch all term for any type of urinary track issue and includes anything from urinary track infection (very common in adult male cats) to bladder or kidney stones. Increased thirst (a good thing) and decreased and painful urination are typical symptoms. The change in diet is to lower ash and magnesium which affects pH and exacerbate urinary track infections. The chemical smell may be from a build up of these chemicals that he is now excreting. You cat may be urinating in frequent small amounts outside of his box because it is painful to urinate so he is trying to hold it as much as he can. Be sure to continue giving him the antibiotics for the full course prescibed by the vet, even if his symptoms improve. It can take several weeks for any infection to be eliminated but you should continue to see some improvement over that time. If he stops improving, there may be something else going on (like a stone or other blockage) that might need to be surgically removed.
FUS is now referred to as FLUTD(feline lower urinary tract disease)
I have a kitty with it too.
Did the Vet NOT do a urinalysis to tell you what type of crystals your kitty has?
If he has struvite crystals they are very treatable with the proper diet.....be sure to NOT feed dry food...needs to be can food as they all have 3x the water content of dry. he needs plenty of fluids to flush out his bladder, the proper can food plus lots of drinking will disolve and flush this type of crystal.
If he has the oxolate crystals than unfortunately diet won't eliminate the problem and kitty will continue to have bladder blockages....this condition requires surgery.
monitor kitties output, he needs to be peeing and lots.
the leakage could be caused by a present crystal(stone) in the urethra and the urine is just bypassing because his bladder is full, this is a very painful condition so be sure he is peeing and not blocked again, if this happens he will need emergency Vet care once again.
keep us informed on how he is doing please, and I wish you 'both' all the best of luck.
sorry I meant to answer your initial question, no the Vet didn't hurt your kitty. manual manipulation won't cause any damage.
I also should mention the Vet may need to install a catheter and leave it in for a few days, cats urethra's are so tiny its difficult to pass some of these crystals a catheter will allow some of the larger ones to be eliminated, I'm glad he did give him something for the pain.