It can also be used when someone is giving something of quantity to another person. For example: your friend gives you five cookies when he has a total of 20, you could say "Don't get short with me" implying that you think that you should get more. Note* This is not a very polite thing to say, you should only use it with close friends or siblings, NEVER elders.

Hi! It mean "Don't be rude!" I have never hear "Don't get short with..." I hope it helps.