What do I do when my stress and anxiety are making me a mean person?

First of all...

You want to identify what the problem is. In your question, I see that you acknowledge life is stressful and your patience is non-existent, and as a result, you are turning into a mean person. So, it seems that the problem is you notice you are turning into a mean person. This is a problem only because you want/value being a "good" person. So, the problem here is that life's circumstances are being allowed to alter us. 

When we allow our circumstances to alter us, we are left to the mercy of the environment as to how we will be that day/week/year/life. One "bad" day or harmful self-indulgence is not the problem. The problem is that when we think negatively to "badly" about ourselves, and we do that 10, 100, 1000 a day over the years, we have an established habit and poor self-image. 

Life's circumstances occur; your choice is how you deal with or see them. Yes, there is a choice in all of this, and you have to notice that despite what you may feel comfortable or familiar with, you can choose not to view negative situations or judgment or indulge the belief, "life will only be better when this thing in my life is over." That last belief is very harmful to people, and it ruins many lives.

Allow the thoughts to pass. 

Your thoughts or judgments within a situation are allowed to exist, just like you are allowed to not judge or live according to them. Imagine the ideas from your life to be like leaves on a stream- there, abrupt, out of your control. Let the leaves pass. Imagine you are in the most stressful of your situations. Picture yourself standing there while the chaos/negativity surrounds you. Imagine your feet in this situation. Imagine you standing there, open hands, hearing everything, yet never at any more peace in life than at that moment. 

Don't let the narrative of your mind tell you how to act. You can allow the mind to speak to your judgments, interpretations, expectations, and the like, but you do not have to let those thoughts define your quality of life. You can choose, yes choose, to see the positive aspects of things and see yourself as an intricate part of an extensive system, very much necessary to the whole of the world. 

Application

There are many approaches to stress management. One is to look stress right in the eye and acknowledge its presence. Personify stress; give stress or anxiety a name in your life. Say to yourself, "oh, here comes _______" when that part of you starts to tell you things. Please do not run from stress or alter your life to avoid it. No, when stress produces a body sensation, or a judgment from your mind, notice that, sit with it, and get used to the pain your mind is telling you to respond to. I am telling you, this will be your bulletproof vest to life when you can remove yourself from the hostage situation in which your emotions and thoughts have you. 

- Luke