Clean and Sober, and Depressed? Withdrawn?

 You are right to be concerned about your brother.  You say that it has been a month since your brother gave up drinking and using cocaine regularly.  I don't know if he quit on his own or with the help of a rehab center or counseling, but his behavior, while upsetting is normal to a degree.  The purpose of any addiction is to keep us away from our feelings . . . feelings that seem overwhelming and unmanageable.  When the addiction stops, we're faced with the very feelings we used the addiction to avoid.  Therefore, it sounds like that is what is happening with your brother.  He needs more than encouragement to go out and be social, he needs support to get good counseling so that he can learn to deal effectively with his feelings, stresses and anxieties in his life. There are a number of possible resources for him to explore, and yes, it's for him to explore.  You can help, but he needs to take responsibility for his recovery and ongoing sobriety.  You may want to sit with him while he makes the calls, or look into what kind of insurance coverage he has, but the calls and appointments need to come from him. 

I don't know where you live, but most states have out patient rehabilitation counseling services available through local hospitals.  That's one place to start.  You don't say how old your brother is, but there are also some programs which are geared toward the young adult (under 21).  You can also explore private therapy with a therapist who specializes in addictions and depression.  It would be a good idea for your brother to be evaluated by a psychiatrist as well, since he may also need antidepressant medication,or even anti anxiety medication.  This, however, should definitely be monitored by a psychiatrist! 

Your brother may also find that neurofeedback can be helpful in changing the addictive pathways in his brain.  Many people also find hypnotherapy helpful in dealing with the underlying causes and needs for any addictive behaviors.  Support groups also are helpful for many people recovering from addictions... You can check out local AA meetings or NA(narcotics anonymous)  meetings in your area.  These are meetings that, if he needs additional support, you could attend some of these meetings with him til he finds the group that best fits his personality and needs.  Remember, the goal is for your brother to take responsibility for his recovery and you are the catalyst and support for his change. 

Since your letter indicates that he lives at home, if there are other family members also living at home, I would recommend family counseling, too.  This can also be done through a local outpatient hospital center or privately, but it will be necessary to have ongoing support for the entire family as your brother goes through the process of changing how he lives his life. 

Please feel free to contact me should you have any additional questions as you move forward.  I am sure that your brother is grateful for your support even if he is unable to express it at this time.  Recovery is a stressful time, not only for the recovering addict but for the people in his life, too.  Please make sure that you are taking care of yourself mentally, emotionally and physically, and that you are getting the support you need to deal with the stresses in your life.