Is it right to say:
Yesterday I was annoyed about commuting to my work because of a big traffic jam.
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I think the expression "annoyed about X" generally means that X is the root cause of the annoyance.
In this case, it sounds like weren't annoyed about commuting, but you were annoyed about the traffic jam.
If yesterday's traffic was unusually heavy and slow, then it might be better to say:
Yesterday, I was annoyed by the traffic during my commute.
But if the heavy traffic happens almost every day, then you could say:
I am annoyed by commuting because I don't like the heavy traffic.
As a footnote, the prepositions by, about, with, and over can all be used with the word annoyed, though by and with seem to be the most common.