I like to say this in jest when cats & dogs munch loudly on their dinner: "Your cat Molly is eating at me again!" I'm not sure what's "off" about it. Is it in fact incorrect, or is it merely awkward?
It sounds like a humorously intentional misuse of the phrase "eating at;" ordinarily when something is eating at you, it means that there is an unresolved situation, and that you are unhappy leaving it unresolved and are distracted and annoyed by it. Your use of the phrase to refer to a pet directing the noise of its consumption in your direction is incongruously literal, and therefore funny.
That particular usage seems to parallel a usage particular to therapeutic psychology and interpersonal dynamics. An example of that might be:
You aren't caring for your mother, you're caring at her, playing the martyr and making sure she knows how very inconvenient it is for you.
It carries the same sense as "your cats are making a lot of noise while eating because they know it bothers me (or because they want me to be very aware of the fact that they're eating and I'm not, etc.)".
If that is the sense in which you're using it, it is not standard, but it would certainly be understood by anyone who has been exposed to, say, Dr. Phil.
"eating at me" is usually used in the context of having a corrosive or erosive effect -- These financial problems are really eating at me (although eating away at me may be a more common form). Your usage in the sense of someone (or something) deliberately directing eating noises, etc. at you is a bit unusual, though valid.
The movie Tom Jones was famous for the scene where a couple used a dining experience -- of eating at each other -- as foreplay.