This is a common side effect of taking antidepressants ( and is especially common with Prozac from the very beginning). These meds can change personality in some people who take them, they can cause violent thoughts or suicidal thoughts or angry thoughts. They can increase anxiety. This happened to me with Paxil and it took a long time before I realized it was the drug doing this -- like you, someone noticed and told me. If the drug is working really well for you otherwise, you might try to focus on this problem and try to overcome it. Because it's been a short time on the drug, it might go away. Or you might have to find a different med as sometimes a med just isn't the right one for us.
I think anger is a symptom of anxiety. Increased aggravation. I'd say your Prozac is not at the right dose and you need a higher one or the wrong med for you. good luck