There are two parts of it...
(1) How you actually deal with that person practically (face to face, by e-mail, telephone, ignoring).
(2) How you deal with the feelings (resentments) that they cause in you. This may seem the least important - but actually it's the MOST important as far as your sobriety goes. Even staying peeved at someone or something that is understandable and justified can threaten our sobriety. As you say you did (and I did most of my life) it's easy to end up drinking through emotions and problems rather than deal with them.
For me personally, learning how to do this is the most amazing part of my recovery so far. (I couldn't have done it without doing step 4 of AA to be honest.)
Hope you feel better soon. Just remember - drinking won't make anything better.