First off, even though you love your dog and everything, if two dogs start fighting, getting in the thick of it will result in you being bitten. Now, that isn’t so bad, but when you throw in a mention of a Pit Bull Mix, it ups the Pain and Damage Ante considerably.
Most of the damage that will occur from a dog bite is by a the person automatically pulling back from the dog, who is pulling away from them. Give the dog your arm/hand/leg and beat the shit out of its face until it lets go. use to be playfully bitten by a german shepard all the f’in tim as a kid. Fall on the ground, you are screwed.
Second, your first instinct to shout at the dog with a basic command was excellent. Established dominence. you stud!
Third, sans pit bull ( a breed I do like alot, but there are too many morons out there with them.) I would probably wade in ( If I had decent shoes on)and kick the aggressor dog in the stomach and grabbing mine by the scruff while shouting “No” and “Go Home”.
Fourth, I would report it to the police, regardless of the outcome.
Sidebar:
When my son was about a year of age and I was out for a walk with him along our back country dirt road, I found myself in the middle of the road surrounded by a pack of beagles.
They came silently, like beagles do when they are not being a bloodly noisy lot, upon us and surrounded us.
I froze. How to I protect my baby from these dogs?
Then, after a moment, the Statler and Waldorf who live in the back of my brain said, " THEY ARE BEAGLES! No one has ever been attacked by a BEAGLE unless they were covered in gravy!"
I stomped my foot on the ground and ZING! off they went, taking their reign of cuteness and stupidity with them.
Damned beagles.