I'm sorry; that's really tough. I told my siblings and asked they not share it with anyone. That didn't happen. They told their significant others. They didn't tell me they did this. I asked them if they did and they said they needed to share it with someone - it was too hard not talking to someone about it.
Then they started challenging me... "Why are you still taking meds?" "Why are you still seeing a therapist?" "You need to change therapists because this one isn't helping." They just didn't get it. After a particularly deep episode that put me in the hospital I allowed them to talk with my pdoc. They have a better understanding now and are much more supportive.
Are you old enough to or do you live on your own? If you are out of the house then just don't tell them. If you are still living at home, just do what you need to do to take care of you and don't feel obligated to tell them. If they ask, say something like ..."I was taking care of something." and try to leave it at that. If they push just stick to "I was taking care of something. You don't need to worry about it."
I wish you luck.