You have a good start with Photoshop and DW. You need a good text editor as well and at least a basic understanding of; Javascript, PHP, SQL, and SSL for your E-Commerce clients. A good knowledge of server administration doesn't hurt either.
The above advice about the "ongoing process' of learning couldn't be more correct. I can only add that design is only one tenth of what i do as a designer. I spend the rest of the time, which means MOST of my time, doing everything else my clients require from tech support to washing dishes....well maybe not washing dishes.
i won't go into a lot of detail about it except to say that on any given week, I may deal with a print house for one client, teach another to set up their e-mail properly, install a script for another and teach them how to work it (even though i'd never seen it before), etc, etc.... none of which technically is web or print design. however, clients require it.
In short almost anything you learn, including "the customer is always right" will come in handy, eventually. 
Good Luck,
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