Let me start by saying this - Nothing you learn / do / read / watch or listen to in order to improve your skill-set in this industry should be motivated by something like "wanting to land a job" or "make more money".
As a designer / developer of any kind you should want to learn something if it feels right and makes you feel nice and fuzzy inside. You can then apply the knowledge and skills you gained in solving problems for users by providing them with delightful interfaces to use (which in turn assure great experience).
Learning web design and HTML (you should probably learn CSS (SCSS) and JS too if you go that route) would not make you a better UX designer. It would certainly make you aware of aspects of design and development you didn't think of before but those skills in themselves make little difference. One can know every language in the world and code down the silliest most unusable application, while someone who had never seen code might approach design in a stellar way.
To me knowing how to program and knowing how to design are two parts of the same coin. You should nurture both of those skill-sets in order to create great products and services.
At the beginning however you should certainly focus on UI and UX. There are tons of great books to read, blogs to browse through and communities to lurk in. And if you've never dabbled with design at all you should take a further few steps back and begin learning about classical design principles like typography, baseline grids, layouts, ratios, proportions, patterns... You should learn how cognition works, how we recognize patterns and why and when we appreciate visual rhythm... Tons of things really.
Focus on your design skills and if you're truly passionate about the craft you'll know when it's time to learn to code.
An agency will hire you not because you know a bit of many things, but because you're very good at just a handful of those. :) Keep that in mind.
Best of luck.