Do you think I'm doing the right thing for my boyfriend?

Okay, you did the right thing at that moment. If he tells you that he doesn't want to date you anymore, you should still try to be friends with him, more if he's doubting everything. I'm thinking that you can pretty much tell when his depression is starting to come back, so you should probably be friends with him, and if he starts to think about suicide you're probably the one that would be able to talk him out of it. It's good that you told his family, and that they're keeping an eye on him, but worry isn't going to do anything for him, just relax and check in with his family and keep living. If he really cares about you, then when the time comes he'll go to you for help because he trust you. Hope this helped, Goodluck.