Hang in there, it's going to be a long ride. Six weeks is like the first season in the 9 to 48 months it could take to get your life back and your beloved well in their heart and well with you. The
infidelity trauma you have inflicted may indeed lead to depression but I wouldn't jump to that conclusion before readingthat link to my infidelity webpages with info on betrayal trauma and grieving. You are both in the first visit of the grieving cycle that travels around Shock, Denial, Anger, Bargaining, Depression, Testing, Acceptance. It takes a while to go around a few times and come to a genuine acceptance. Depression is a natural part of grieving, not a feeling I would recommend medication to dull. However, clinical depression is a concern and can be described as 'fragility, brittleness, lack of resilience, a failure to heal, with a loss of any emotion but guilt, of any desire but to stop'. PTSD is also a concern and I hope you both have access to a clinical psychologist or equivalent to help differentiate normal grief from clinical depression and PTSD. Both untreated can take up residence in the brain and there are effective interventions for both. Couple therapy is a more effective treatment for depression than anti-depressants - London Depression Intervention Trial.
Since alcohol has been part of your story, I wonder how much you have used drink and sex to alter your moods, to calm yourself or to manage the pain you have been carrying for decades. And maybe also you have experienced difficulty in impulse control and frustration tolerance. Without sex and alcohol to medicate your body, you are probably struggling to soothe your nervous system in a legitimate way and that is really hard work. I hope your therapist is teaching you safe ways to calm and self-soothe and that your partner has access to the same resources.
It's a long journey but the reward is to be truly married for the first time in your life, with your dearest friend your partner.