If the statement is a moral normative claim, I might rephrase it a follow:

If others have it worse than you, you oughtn’t complain (or ought to perform x)

There’s nothing inconsistent about it. If children starving is worse than you, it would simply follow that you oughtn’t complain/perform x (a version of modus ponens). However, we can assess the soundness of the two premises—that is, their truth or falsity. First it involves affirming that starving children is worse than your current state of affairs, which involves how you define “worse” (or, more generally, a “bad state of affairs”.) Without going into meta-ethics, most people will simply concede that that starving is a worse state of affairs than what is (presumably) you being well-fed (in a non-academic setting, this will almost certainly gain universal assent.) Instead we may ask for a defense of the premise “if others have it worse than you, you oughtn’t complain (or ought to perform x).” A defense of such a principle will likely amount to showing that it follows as an instance of your most general principle that dictates what actions you ought and ought not perform. So, I can’t state any direct informal fallacy that it may be committing, but if you want to be a bit more rigorous in assessing the argument, ask for what dictates (in the general case) when a person ought to perform a certain action. Is it consistent with the categorical imperative, Bentham’s greatest happiness principle or some variant, etc.? However, if an enquiry into the land of meta-ethics and normative ethics isn’t your cup of tea, you could demand the relevance between having something worse than you, and having to perform some action (still an assessment of the soundness of “if others have it worse than you, you oughtn’t complain” as a moral principle). Then state some counter-example where someone clearly has it worse than you, but it is clear to us that you ought not have to perform the said action. (For instance, someone’s entire family was murdered, which is worse than the single murder of your mother; therefore, you oughtn’t complain about your mother’s murder/go about your day as usual. Clearly, this won’t gain assent, but if the aforesaid moral percept can be extended to include instance beyond food and starvation, then it would follow.) The above example, I think shows that at a kind of “common sense” level morality, there clearly seems to be some instances which, despite others having it worse, we are justified in pursuing our desires—which is probably what I’d say in an “everyday” argument with someone as a rejection to that "argument". (Though, as it is stated above, it is not in the form of an argument.)