Welcome to the forums. I'm really glad that you have felt able to reach out and share what has been happening for you.
I am really sorry to hear that you have been hurting so much. It sounds like you are in quite a dark place and that things are getting increasingly difficult. You are not alone in what you are experiencing, unfortunately it is not uncommon for anxiety and depression to coexist - this can make getting through each day feel especially hard. It is tough when it affects every aspect of your life, but please do not feel that hiding it from your children is the only thing that you are doing right. There is not really a concrete right and wrong, you are going through a lot and depression and anxiety can make just functioning and looking after yourself difficult, let alone caring for others that depend on you. From what you have mentioned, it sounds like you are really trying everything to give yourself the best chance of improving - seeing your GP, making an appointment with a psychologist, and having the insight to see that you were using alcohol to cope and trying to stop drinking as a result, that is tough but you are clearly motivated to make changes and this is really important. Is there anything that helps you to feel better, even only for a little bit?
Different things work for different people, some of these may not be your thing and that is more than okay, but here are some suggestions you may like to try for when things feel really overwhelming or difficult: journalling - writing down your worries and thoughts and what is going on can help organise your thoughts and get them out of your system and can help you see your thoughts from a different perspective, being outside in the sun, calling a friend or loved one, listening to your favourite music, watching a favourite movie/show, washing your face with cold water, having a bath or warm shower, playing with a pet, hugging someone or a pillow, calling a helpline (Lifeline is 13 11 14), making a cup of tea or hot chocolate. You may also find grounding techniques helpful - they focus on shifting your focus away from your mind and back onto the present, they can involve controlled breathing techniques, meditation exercises and sensory exercises, it may be worth looking up grounding techniques to have a try.
Please do not hesitate to reach out when you feel up to it. We are here to listen and support you. Take care and give yourself the time and space that you need.