You aren't the dick here.. its RUDE to allow your dog to run up to a dog on leash, a dog doing close heelwork, a dog clearly training with their owner.
Everyone saying 'don't pick up your dog'... you realise that when there is a huge size difference, a dog like a Dane can kill a yorkie or a chi simply by splatting it with a paw, there doesn't need to be any aggressive intent there!
OP, pick up your pup where you need to.
Understand that, picking up a dog that hasn't seen you coming may startle them, so train your dog to paws up on your leg on cue and be lifted fully aware of whats going on. Reward them using high value treats for this, bothfor the paws up, and the lift.
Also know that SOME dogs will find a dog being lifted off the ground something of a trigger, and it MAY cause that dog toleap up at you and grab for the dog you have lifted - sometimes it is safer not to pick up, sometimes its a risk you have to take.
Treat bombing is a good tactic to redirect an oncoming dog, but I would reserve this method for after you have asked the other owner to recall their dog, and after you have tried walking back to them so they can collect their dog.
Another option is the Voice of Doom... but you'll need to prepare YOUR dog for this so it doesn't upset them, so just pair the VoD with a scatter of high value treats, at home, in the garden, then in the park when its quiet, before trying it on an actual incoming dog. Something like a big deep NO! Or even a SIT! can help.
Meanwhile, before you get to training, make a habit of pairing the sight of other dogs with yummy treats, for a Chi since their fill level is low, a good option is Primula cheese, direct from the tube. A little lick of that is a really strong reinforcer. Remember you are pairing your dog SEEING the other dog, you are not distracting your dog by using the food so that they don't notice!