Well at first you said web designer and now you are saying web developer which is it? A web designer can be very different from a web designer. Of course there is some overlap but one is more programming focused and the other is more design focused. An appropriate degree for someone who would like to be a web developer would be a Computer Science degree. Where as a proper degree for someone who would like to be a web designer is a Graphic Design degree. Notice that I didn’t recommend Web Design because just everyone in this industry thinks those are a joke. Either a CS or Graphic Design degree depending on where you want to be in the end a programmer or designer.
Having said that Junior positions are typically 2 years of experience. Experience in eye being working with a company in some type of position where you are exposed to other developers/designers with differing experience levels. So not “freelancing” or to put it frank whoring yourself on sites on contest or freelance sites right out of the wom.
You will be hard pressed to be employed as a entry level programmer/developer without any degree. Designer is a little different but still you are going to need pass HR and portfolio. Though design is very much aesthetic and forming an eye/brain for design is a process. A process best guided by someone who has been in the field. To judge your own work without any experience is pretty much anomaly since you wouldn’t need to learn if you already knew these things. Simply relying on feedback on forums and/or “clients” is a very fragile and volatile way to conduct the beginning of an education in a career.
I do think it would be *easier to get a design job over a programming one without a degree. Though design salaries are also typically several 10s of thousands dollars lower than programming jobs. Typically anywhere from 20 - 50K difference depending on experience and location.
However, I believe what you might be referring to is more of a front-end web developer than “designer” per say. Pretty much a front-end developer who is able to create mock-ups as well as implement them in HTML/CSS/JavaScript with some server-side knowledge.