I'm not sure if I can help but I definitely sympathize!
I have had MANY dreams about pets (past and present) where I realize I forgot to feed or take care of them, or I am trying to take them away from some approaching danger and have to make sure I have enough food and water from them.
I've also dreamed that I've accidentally hurt/killed one of them.
Your interpretation sounds reasonable to me too. I think mine have to do with the fear of not living up to my responsibilities, and pets are so innocent and completely dependent on you.
On that note I think I'll go make sure my kitten has fresh water...