I hate to be amongst the mass here because I know it's not what you want to hear. But it's true. EVERYONE has problems in their lives, and you have to learn how to manage your problems and your obligations. Just do as many of your assignments as you can, focus on making sure the bigger ones worth more grades are getting done, and if some have to be late, just go to your teachers, tell them you are getting it done and that they'll be in soon, and work on it. You can't realistically expect your teachers to NOT penalize you just because you are having some trouble. The standards are what they are for a reason.
I don't have anxiety or depression but I do have ADHD, and in high school I'd just wake up early where necessary to do/finish work, if I had a big project to finish I would pull an all nighter if I needed to. I learned very quickly that unless it was for a very good reason (I was sick etc) it was just better to say "it's late, I'm sorry" and leave it there, if the teacher gives a flying fart in space about WHY they will ask. But my time management in high school wasn't what it was now. And if it had been, quite frankly, I probably could have avoided losing so much sleep trying to get my work done. So that being said time management is also a big thing, you should make a schedule and leave time to study accordingly. I manage to work out 6 days a week, cook, do all my house work, and volunteer (9-10 hours a week) and get plenty of good grades and I still have free time AND get to sleep plenty. And that's not me trying to brag or something. It's just that THAT is what mastering time management allows me to do. If I couldn't manage my time shit would seriously slip through the cracks. If you
PM me I can help you with designing a general schedule.
Aside from time management you should make sure you know when to ask teachers for help. I don't care if you are to stubborn to LIKE asking for help. Quite frankly your alternative is to get shitty grades when you don't understand an assignment properly. So choose as you will, but I recommend just asking for help.