羽目になる: ending up in an unwelcome situation
Recognize dissatisfaction or difficulty in an outcome and distinguish it from the more neutral ことになる.
Viewing an outcome as a predicament
準備を怠ったため、全員の前で謝る羽目になりました。 means that neglecting the preparations left the speaker having to apologize in front of everyone. It does not merely schedule an apology; it evaluates the outcome as unwanted.
羽目 is read はめ in this expression. An earlier mistake or circumstance leads to a troublesome situation. What matters is that the speaker regards that situation as unwelcome.
Separate the action from the time the situation arose
The expression follows a dictionary-form verb, as in 歩く羽目になる. 降りるはずの駅を乗り過ごし、遠い駅から歩く羽目になりました。 means that missing the intended stop left the speaker having to walk from a distant station.
なりました places the development of the predicament in the past. The action itself may still be scheduled for later: 明日も働く羽目になりました means ending up having to work tomorrow as well, not having already finished tomorrow's work.
Compare the perspective with ことになる
明日も働くことになりました。 can neutrally report a decision or situation in which the speaker will work tomorrow as well. 明日も働く羽目になりました adds the perspective that this outcome is troublesome or unwelcome.
羽目になる is not a good choice when the intention is simply to report a happy, unexpected outcome. The same event can be described with it if the person affected finds it troublesome, so consider the speaker's evaluation rather than only the event's category.
Does 明日も働く羽目になりました。 mean that tomorrow's work is already finished?
Show the answer and why
No. It means that the speaker has ended up in the unwelcome position of having to work tomorrow as well. The past in なりました refers to reaching that situation, not completing tomorrow's work.