OK, here’s my stab at an answer. If anyone knows better, please correct me by all means!
I don’t think that any feelings are in and of themselves sinful. Most of us don’t like the way anger or sadness, for example, feel, but they pass in and out of our lives. We who are scrupulous can interpret that discomfort as sin. However, negative thoughts, if nourished and brooded over, can sometimes turn into temptations to really sin, which, if we follow them, can be venial or mortal, like any other sin.
So, if your anger at God swirls around in your head and makes you stop praying or attending Mass, or leads you to hurt your loved ones (for example), then it would indeed be sinful and, if mortally so, it would damage your relationship to the Church until you would go to Confession.
So – and I advise myself strongly here, too

– it would probably be best to pray about your anger (after all, He knows about it already and He’ll probably help you with it if you ask) and do your best not to dwell on it, as it can only compound itself and become more and more of an occasion to sin.
I’ve done a lot of thinking and praying about forgiveness, which is a related subject, and what has helped me the most is the understanding that: 1. I cannot pray for the offender and at the same time hate and fail to forgive him, so if I sincerely pray for his well-being, I am in the process of forgiving him. And, 2. We can always ask God to help us want to forgive and to show us how to do so. It’s His command, so He wants to help us.
I’m sorry if this is more/different than what you were looking for. Hope it helps.
Kristen