You make me feel hopeful about my own academic future. I'm also 28. During university I fell into a severe depression. I managed to finish, but did not go on to grad school like I planned. I graduated 5 years ago, and have been battling depression since then. I'm doing a lot better now, and I'm trying to get the courage to just apply. You can do it. And like others have posted, you have the advantage of being older and knowing what you want to do. You don't have to deal with the confusion that comes with being 19 or 20 and you can just focus on what you need to do. Do you go to therapy? Maybe they can help you on techniques to help you when you feel your anxiety start to flare up.
All the best, Tigerlily