The right of Redress is key and should be used, but it should not be abused.
In considering wether to Redress you need to be able to state that your have been wronged, explained what the effect of that was (in factual not perceived terms) and state how you want that wrong to be put right (hence the term redress of complaint). You cannot redress because something has happened to somebody else. There is also a time bar to redresses of complaint (3 months (if my memory serves me correctly) from either the incident or from when you learned of the incident). Though I have know Redresses be processed even if they are out of time.
So you will need factual evidence that your career has been affected (not just you think that you should be a group captain by now). Then you need to decide on what remedy your seek. You cannot just ask for an apology that does not put anything right.
You unit P staff should be able to help with the drafting of it and steer you if they think that a Redress is warranted (and not just completely hatstand).