Web design is one of those fields that changes so quickly that a degree IN web design in my opinion is a waste. But that doesn’t mean a degree can necessarily be a waste.
Degrees are just tools. We’ve gone to this place where we think that the degree is the goal, but it’s not even the beginning (it’s only the foundation of a very limited beginning). So think about what a degree is going to do for you, in your field, as a simple tool and I think your perspective changes to be a bit more realistic. Personally I’ve always been a much bigger fan of certifications than I ever have been of degrees. Certifications seem to be aimed at giving professionals the tools they need to get right back into the field with more knowledge. Most degrees I think are bloated because they are designed for people that come out of high school and need a far more rounded educational experience to make up for a lack of any actual functional experience.
Consider also that a degree and education are not always the same. Those that are passionate about being the absolute best at what they do and they love it WILL educate themselves without prompting. It’s just natural. We consume books and watch webinars and listen to podcasts and try code and read articles and take tests and build shit all the time.
The best thing to do I think is to first figure out if web development, design or UX is for you. Figure out if you love it or not. If you don’t, then find that thing you really do love. If you find that you love this industry, start building things and be a consumer of knowledge and you’ll quickly start seeing how much there is to learn and how little time you actually have :)