If it is a recurring symbol it must be very important! what do you associate with alligators and reptiles in your life? do you have any memories involving them?

without more context it is hard to interpret, but here is what i think:

since the lizards are a plural group rather than a single character, they may represent a concept or something recurring. In the dream, they kept growing if you didnt kill them while they were small. maybe you feel overwhelmed in real life constantly stomping out small fires before they consume you. or maybe its more abstract and you have to constantly 'kill' certain subconscious thoughts or desires that keep springing up. The last one getting away may show that youre not able to stay on top of this issue and you feel it slips out of your hands.

once you figure out what the alligators represent i think youll have an easier time interpreting this dream.