Would a person be considered a "braggart" if he reminded another of a good deed between them to counter an accusation of not doing good, especially after that other person wronged him and did not apologize?

The blameworthy mann (reproachful reminder of a favor) is the mention of a blessing or good deed to make the recipient feel indebted or to reprimand them, and it invalidates charities. However, mann is permissible when there is a need for it, such as with someone who denies a blessing or good deed, or to remind someone who needs it so they do not fall into something forbidden. Therefore, reminding a person who denies kindness and repays it with ingratitude and abuse is permissible, and it does not fall under the forbidden mann.