Nice, I just noticed a couple of really minor things:
I would combine “Suddenly, I heard a door swing open behind us. It banged against the wall.” so it reads, “Suddenly, I heard a door swing open behind us, banging against the wall.”
“When I turned to see who it was, Tori wobbled towards us…” can be changed to “When I turned see who it was, I saw Tori wobbling towards us…nine months pregnant.”
“Shh!” he warned, "I think there were more gunmen at that end of the alley, too.” Using the dumpster as a cover, pulled out his gun. He took off the safety, aimed and fired a couple of bullets. Elizabeth could tell he made his target by the yelp of surprise and pain from the enemy.
“Alright, stay close. Just follow my lead.” he said. And with that, they ran out from behind their cover, going the direction that Max had just been firing at. A few bullets whizzed past them, narrowly missing. One bullet that was aimed directly at Max’s head was blocked when he swiftly used his briefcase as a shield, simultaneously firing his own bullets.
"There!” Max spotted more crates and boxes in the alleyway that created another hiding spot, and pushed Elizabeth unceremoniously towards it. Understanding what he wanted her to do, she took cover.
But this time instead of hiding with her, he kept running towards the source of the gunshots.
(Don’t worry, she seems kind of demure atm but this is a bodyguard story, she’s letting him do his job. But also, she’ll kick butt on her own later in the story)