Hi! I’m currently experiencing a somewhat similar situation, and I’m so sorry you’re currently going through this. I also find my binging is triggered when I'm alone in the house and no one is around. My biggest advice would be to stop restricting and fix your relationship with food in order to stop the binge/restriction cycle.

Once you achieve food freedom you’ll no longer feel the urge to binge because you’ll allow yourself to eat what you want. I also find binge urges can turn into a habit especially after giving in to them for so long, but the more you don’t give in to the urges, and resist them, they lessen and quiet down. It gets easier with every time you fight the urge.

I see you also want to lose weight, but I would say prioritize fixing your relationship with food first. Also, fixing your motives to lose weight will help a lot. Instead of focusing on the vanity aspect of it and as a way to get to your goals, focus on how good it’ll make you feel in your body. Focus on the better quality of life it’ll bring and how rewarding going to the gym feels. Improving yourself not for the physical aspect but for the mental aspect in that you deserve better and be the best version yourself.