I suffer from chronic anxiety. Will this alter how I go through the forgiveness process relative to those who are not suffering in this way?
Sometimes our anxiety comes from not feeling safe. Sometimes our not feeling safe emerges when others treat us unfairly. In other words, you may be expecting poor treatment from others now, even those who usually are fair.
A first step may be to think of one person who may have hurt you and at whom you still harbor resentment. You can forgive through the exact same pathway as described, for example, in the book, Forgiveness Is a Choice. With anger lessened, anxiety can diminish. Of course, this will vary for each person. We have to be gentle with ourselves as we learn to forgive, to give up anger, and to know with some confidence that we can meet the next interpersonal challenge with forgiveness, helping us to meet these challenges with less anxiety than in the past.
For additional information, see Learning to Forgive Others.