Welcome to the forums and well done for taking a big step forward - getting it out of your head and onto a page is a a great start.
I am going to say to you that this "Like I said big sob story right? I know there are worse off than me" - No. No discounting yourself or your feelings. Your feelings are valid and, holy hell, a lot of us are feeling the mental health effects of the pandemic. Even before the pandemic, there was a lot of stigma around mental health and this attitude that there are "people worse off, I should suck it up". However, what we've seen is that those who have tried to keep going and keeping their feelings all inside, are the ones who are hurting the most, because they are never allowing themselves a chance to feel, rest and heal. And that is so important.
I want you to focus on baby steps. Can you book a day or two off and have a mental health day(s)? Can you ask someone to look after the kids for a few hours? Or even a few days? Sometimes catching up on rest (not depression sleeping, but proper rest and quiet time) can give you the circuit breaker you need to find some energy.
Re the psychologist appointments, have you thought about using the webchat function on the beyond blue website (if your phone is not working)? The people you speak to are trained mental health professionals and they might be able to provide you with some helpful tools. You'll find the link on the top right of the website. They are really caring and I rate them highly.
Have you also considered seeing your GP and considering your options, re the depression? Maybe going on some medication will assist in helping you get out of the darkness of depression, or have you not slip in any further.
Please know that we are here to chat with you and support you. We've all experienced these feelings at some point and it is sometimes so difficult to get your head out of the depression fog. That's why I say "baby steps" - just one step forward (like you posting on the forums) is progress and it's a step in the right direction.
If you feel like you have the energy, I really recommend the CCI workbooks and info sheets, just in an effort to stop yourself having those depressive thought spirals. I've used them before and, for me, they've made a difference: https://www.cci.health.wa.gov.au/Resources/Looking-After-Yourself/Depression
Sending you a big hug. Here if you want to chat more.