ALOT of vet cleaning solutions are made with alcohol as a drying and disinfecting agent, as well as tea tree oil, mineral oil, etc for soothing it or relieving itch. A mix of these to ingredients is probably the cause. The oils used can make the hair greasy/oily thus binding the coat hairs together.
I would try simple clear dish soap with no additives or scents, like clear dawn, with warm to cool water (the hotter the water the more damaging to the skin as well as it's fur). It's a degreaser which will remove the oils in the fur which may be the cause, but more importantly it's very safe for cats and kittens. It's even used for oil spill animal victims, and used to treat fleas in kittens and puppies that are too young for pyrethrin exposure. I would try this, and make sure it's rinsed out completely until there are no suds or bubbles. It being a degreaser should help with the clumping, and should make it much easier to gently comb out any remaining tangles.