Is anger a sin?
Anger can be a sin if it is excessive such as when it becomes rage. I think it can also be sinful if it is unjustified but I am not 100% sure on that last point.
Not per se, no.
Anger can be morally good. Jesus became angry and drove the money lenders from the temple. Rightous anger (or indignation) is permissible or even good. When anger seeks just punishment or correction of wrongs, it is acceptable. When it goes further than this, it is wrong. Here is a reference that may help:
Anger can also be considered a merely human emotional reaction, and as such is neither good nor bad, but it is how we respond to the feeling that is important.
Here’s an example: someone does something that angers you and you get angry and yell and throw/push stuff, etc.
Would that be a sin?
I don’t like the sin/no sin paradigm. I’ve no idea if what you’re describing is a sin, but whatever it is you need to strive to overcome it. Drinking 15 liters of Coke a day might not be a sin, but that’s not a great idea either, get my point?
If you have that kind of reaction where you are angry and then do not control it and the results are yeliing and then pushing and throwing stuff, then yes, you are"sinning".
But that kind of reaction is more of a character flaw from our fallen nature. If you have a temper problem, speak to a priest and get some help. Likewise, because your post is unclear, you do not have to be the at the receiving end or someone elses lack of control and temper and anger. That is called abuse and if you are in an abusive relationship or home, get out of it and look for help.
Jesus got angry and exhibited rage, when he turned over the tables at the temple and dumped out the money and used a whip to drive people and animals out.
But is he not supposed to be sinless?
Yet, he felt and exhibited anger (and I don’t think he apologized to anyone for it, right?)
That sounds like Jesus in the temple. So in that particular case, no.
It may be sinful in any given specific example, but as a generalisation we cannot say.