There are only two basic answers to the question "You aren't hungry, are you?" : they are "Yes, I am." or "No, I'm not." Similarly, if your mother said, "You are hungry, aren't you?", the two possible answers would also be "Yes, I am" or "No, I'm not". As you can see, the Yes/No word is in accordance with the statement it accompanies. If you say "Yes", this usually accompanies a positive statement. For example, "Yes, I can", "Yes, you do", "Yes, they have", "Yes, it is" and so on. Likewise, if you say "No", this generally accompanies a negative statement. For example, "No, I can't", "No you don't", and so on. In English, it is not normal to follow "No" with a positive statement. Responding to your mother's question by saying "No, I am" would sound very strange to an English speaker. Here's the problem. I think you are interpreting the words "Yes" and "No" as being the same as equivalent utterances in your own language. I suspect that you want to say "No, I am" because ( in your mind) the word "No" means "No, mother, your statement is not correct" and then you go on to explain that you are actually hungry. Unfortunately, that isn't how it works in English. In English, the 'No' or 'Yes' at the beginning of the answer has nothing to do with whether or not the question was phrased in a positive or negative way. Whether you say 'Yes' or 'No' depends on whether the statement which YOU are making is positive or negative. I hope that makes sense.

Yes, I am hungry.

If you're hungry, then the answer is "Yes". It doesn't matter if it's negative ("Aren't you hungry?") or a tag question ("You're hungry, aren't you?") ("You're not hungry, are you?"). In any of its forms, a yes/no question always has the same answer. "If the answer to all of these yes/no questions is the same, what's the difference between these different questions?" The questions reflect what the speaker thinks he/she knows. Remember, your answers to these questions will always be "yes". (1) "Are you hungry?" The speaker has no idea if you're hungry or not. (2)"You're not hungry, are you?" The speaker thinks you're not hungry, so this begins as a statement ("You're not hungry."). Then, the speaker decides to check to see if he/she is correct [",are you?"] (3) "You're not hungry, are you?" Similarly, The speaker thinks you have just eaten and thinks you are not hungry, but he/she could be wrong. (4) "Aren't you hungry?" The speaker is surprised after he/she finds out that you don't want anything to eat.