What worked for me was getting a psych referral to an addiction specialist who strongly suggested inpatient rehab. I did more in rehab than just detox, it gave me a safe place to kickstart my sobriety, introduced me to AA, and got me to make a plan for recovery. After I finished that, I returned to my psychiatrist and we worked out a medication plan to deal with underlying mental health issues. Naltrexone was discussed, but we agreed that my early sobriety seemed strong and would add naltrexone if I relapsed. I'm now attending an 8 week outpatient program which is teaching me how to deal with negative thoughts around both addiction and bipolar depression, and I'm attending a few AA meetings a week.
Some or all of these may not be available to you, but medical should cover a primary care visit and a psych consult. I was a mess at my initial consult and in the depths of addiction, so you don't need to be sober for this. There were a number of people in rehab on medical, and they will work with you on insurance. I understand there may be other reasons why inpatient rehab may not be an option, but I would strongly suggest seeing a psychiatrist that specializes in addiction and can work with you on a medical treatment plan, at the very least.