What is it called when you raise a problem and someone else makes it seem like you're entitled by bringing up something far worse?

Solution 1:

This is the fallacy of relative privation, which basically argues that you don't really have a problem because there are other people suffering from a much more severe version of the problem.

Here's a quote:

The fallacy of relative privation, or appeal to worse problems, is an informal fallacy which attempts to suggest that the opponent's argument should be ignored because there are more important problems in the world, despite the fact that these issues are often completely unrelated to the subject under discussion.

Solution 2:

Whataboutism

To answer the question directly with a single word, I would say this is an example of 'whataboutism':

The practice of answering a criticism or difficult question by attacking someone with a similar criticism or question directed at them, typically starting with the words "What about?"

(From Cambridge)

To rephrase your original examples:

"These working conditions are subpar. We don't get any breaks." and then someone else says "You're entitled. What about people who work in sweatshops!"

"I'm hungry." to which a parent might reply "You're not hungry. What about the starving children in Africa?"