May I ask why you started out in web development? What drew you in, what did you love? Have you been doing it professionally for a couple of years and how did that work out?
Looking at it somewhat coldly, your skill set is not adequate for today's projects. You already know that. Do you feel that these depression symptoms are the result of your struggle to improve your skills, or were these feelings already present (caused by something else) and as a result, you are having a hard time improving your skills? Or alternatively, is the mismatch between your skills and the needs for today's projects causing the depression symptoms?
Imagine for a moment that you have all the skills necessary for the job. You are good at what you do.
1) Would your depression symptoms disappear? Or do you need help?
2) What does your job look like? Describe what it is. Do you like it?
3) In what direction would you like your job to evolve next, i.e. front-end? back-end? down a specific specialization?
4) If you had the necessary skills, would you rather do another job outside of development? What kind of job?
Basically I am trying to help you work out what caused your depression symptoms and if you like this profession enough to persevere. Secondary, I get the impression that you are not clear on what skills to learn and why. I know from personal experience that "I need to learn this skill because I have to" is not helpful. The motivation just isn't there. It can make you feel needlessly stupid too. I also know how hard it is to figure out what you need for what and why. That too depends on where you would like to go.
Finally, I would like to say that I symphatize. Web development is hard! I have been doing it professionally now for 12 years and I have been asking myself whether web development is for me countless times. It certainly is a lot harder than it was 10 years ago (or I am really getting old!). I am of the opinion that it is becoming more and more impossible to be an all-round web developer and actually be good at anything. Specialization is necessary. The split between front-end and back-end web development is only the beginning. Right now I am doing more or less okay (ehm... okay, I am currently at home with a burn-out, so maybe not THAT okay), no immediate need to call it quits, but I am very much aware of the need to either go deep and all-in or get out. And to be honest, if I knew of a way out I would probably take it... but I digress.
I hope I could help you out with a few questions to ask yourself. Best of luck!