I would try to stay on your side of the fence. What, tangible, do you hope to gain from self-disclosure? Work on that rather than worrying about what others will think of you. You probably should ask for more time or what it is you want before you start on an assignment, rather than not complete an assignment and then say it was because of your illness. Be clear you are asking for tools (time), not an excuse as to why not being able to do the work is not your fault/responsibility and you should be given another chance, etc. If you have trouble doing the work because of your illness, perhaps you should concentrate on getting better before you try to do that particular work.