Indignant means feeling or showing anger because of something that is unfair or wrong; especially, because of an unjust, mean treatment, or action: “She was very indignant at the rude behaviour meted out to her by the officer.”
Indignity , on the other hand, is a behaviour which offends, humiliates, or insults: “The principal passed through a great sense of indignity when the students raised slogans against him in his office .”