i think it means that you are trying to run away from something in your lifetime and maybe you're worried that its not yet over? and dont worry about your dog being shot, in asian cultures if someone gets killed, then that means that the person is actually really healthy in real life.. and i think that good luck will come to the person (in this case, your dog) soon
btw your dreams sound a lot like the ones i used to have, and its weird because i know im dreaming too! i have to tell myself wake up wake up wake up!! this prob sounds weird but what works for me is if i am in a high area like a building or bridge, i just "jump off" and then i instantly wake up.. maybe try that next time if this happens?