No, education is not necessary, the more nobody will give You this education a web designer. In this case, I would prefer self-development.
Exactly what you need to do:
30% theory, my list of books:
Jakob Nielson, "Web Design"
Steve Krug "don't make me think"
Mike Monteiro, "Design is a job"
Donald Norman "Design of everyday things"
Victor Papanek "Design for the real world"
Genrikh Altshuller "to Find an idea"
37Signals "Getting Real"
Jeff Raskin - New directions in computer systems design
JEF Raskin - About the interface
Bruce Tognazzini "the Main principles of interactive design"
Jan tschichold's "New typography"
Emil Ruder, "Typography"
Nora Gal "the Word of the living and the dead"
Sasha Karepina "the Art of business writing"
Muller-Brockman's "grid in graphic design"
Draw everything that comes to hand, pererisovyvali templates are very helpful, do personal projects, that just came to mind, in the end, take the orders.
10% of inspiration:
Every day, before starting any work, look into: