Lots of great answers here. I'd like to add-
Many people who go into UX Design come from tons of different backgrounds. I've seen people switch into it from Psychology, Marketing, Copywriting, Development, and even engineering. Anyone who thinks they know how to empathize with the user. I myself came from a Graphic Design background.
The role of UX Designer is a combination of skills. First and foremost you need to know how to communicate clearly. You'll need to negotiate and navigate between design, development, user needs and business needs.
download bmml source – Wireframes created with Balsamiq Mockups
You need to know how to justify all your choices. Especially if you go down the visual path of UX, as you'll be tested constantly on how you handle constructive criticism. It's all about
Another concept to be aware of is a lot of job descriptions combine UX/UI design, or UX/UI development. Many companies may not have enough work for just the one role. The companies may not always be small, but if your team is small, be prepared to step up.
When I started my career, I decided to diversify as a Web Designer. That meant design and front end development. It got me a lot of experience because I could fill a lot of roles at once but I did not enjoy development. The moral is to go with what you enjoy. Strive to do what you love to do. There is always a way to get the most happiness in your career and get paid for it too.
For me, now that I know more about my role with experience, I can afford to choose the type of role I grow my career in. I chose to drop development and only do ux and design. But knowing development has helped me design feasibly.
Some people choose to specialize in UX. Some in development. You don't have to do development, you could just stick with visual.
Definitely be prepared to multitask. That tends to be the expected thing.
Here's a Venn diagram I made for my blog:
You can read the article I wrote last November on the topic:
Hope this helps you with your career choice.