Sorry to hear he was late on his shots, but don't be to hard on the breeder. Obviously he was doing something right to give you such a beautiful little guy. Also, shots aren't a broad spectrum protection...they only cover a handful of common problems. Infections, in particular, have a lot more to do with an animal's ability to fight off bacteria, which is an area where kittens are lacking. Don't worry about it, though. You are obviously on top of your kitten's health and treating the problem. Getting/giving the drops may seem traumatic, but I'm sure it looked very similar the first time you were given daily medicine for a cold or ear infection (I know I used to hate it). Remeber, cats can be just like a kid in some ways....sometimes they get sick, no matter what. The important thing is monitoring their health with regular vet visits (and your intuition) and getting him care when he needs it.
I feel your pain, though, in terms of sick kittens. I've had a little one, Lola, who has had varying degrees of diahrrea for a month...we've been trying lots tests and treatments, and she's getting better (she has something of a complex gastrointestinal history, though). She's been to the vet so much that one of her favourite toys is the cat carrier! She likes to shut the door when Sammy goes in and then stand on top of it for some reason....anyway, enough about me. Keep us updated with Charcoal! I'm sure he'll be just fine.