Am I allowed to be angry at God?

Yes. Scripture is full of it, and the anger was not removed before it was written down. Anger addressed to God is a form of relationship; polite silence at a distance is not more faithful, only quieter. Say what you actually think happened. Say it in your own words, even the ones you would not repeat to anyone. The tradition has always had room for the one who shouts and stays, and it treats the staying as the whole point.

The old word for it is taanah — a claim, an argument brought before God: the patriarchs and prophets argued with heaven, and it was counted to them as closeness, not sin.

From the sources “How long, O Lord? Will You forget me forever?” — Psalm 13