Congrats on the award.
My colleagues and I have worked in ecommerce for many years and therefore encountered many good web designers - mostly on the agency side (working for a creative agency) rather than in the client side (in the company itself running the website) - however, the good ones always quickly progress from "basic web design" to more complicated design projects that go beyond just web page design - or get heavily involved in team leadership or client account management - and even progress up into the creative leadership roles. bear in mind that you will also need to be open to understanding Business Management skills when you get to this level. i.e web design is a great stepping stone into any kind of broader "digital" role (which has a very broad meaning nowadays)
Also - bear in mind that there is a very strong link between design and the whole world of usability and customer experience (CE), which is an industry / career in its own right. Many functions rely on design and CE skills for developing new products, services, apps, etc
Think about what you really enjoy doing with your web design - is it the coding itself or the creative part - or the joy of seeing the experience you have created that people use .. this could help you guide your career path