What's up, fellow CogSci/HCI 3rd year!! I'm on my phone, but I'll try to help you as best as I can. None of my internships or lab positions on-campus are paid, but I just landed a summer UX internship with a huge company in the Bay Area that is providing my entire summer housing for me in addition to $35+/hour salary.
Think about your intentions. I know you want some free spending money, but are you more concerned about how a lack of jobs/internships will look on your resume or do you truly need the money to spend? It's tough to work for free, I know, because I work up to 30 hours a week at two different places without pay, but the experience and side projects that these opportunities have given me have really paid off.
It sucks working for free and I totally get it. My immigrant parents make less than $40k/year and when I see the loans racking up on my student account, it's painful. But it pays off. UX used to be really big a couple of years ago. Apple came to UCSD and told all UX designers to skip the line in front of all the software engineers. I'm not trying to say that the bubble has popped, but tech companies these days definitely don't share the same sentiment. Talking to Microsoft at the fall career fair, they specifically told my UX friend that that they were looking for "programmers only".
I agree with another redditor in that you should probably try to find a low commitment job like tutoring. The money isn't good, but it's not as high strung and that way, you can focus on your classes.
You are definitely right in that we are competing for these jobs against CS majors and actual visual designers, but the advantage that we specifically have is our formal training in critical thinking and grounded research. That's why I think you should really give your all in your CogSci classes. I read that you're taking COGS 102C next quarter, which is a great opportunity for a side project to put down on your portfolio (which is ultimately bounds more important than a resume).
I know this post may sound discouraging, but I really think it's in your best interest to think towards the future. If you can, definitely try to shoot for a front-end internship/job! BUT if not, focus on finding a low commitment job that keeps you free enough to develop the specific skillsets we need through our core classes. Those are what ultimately make us stand out as CogSci majors applying to UX positions, and we have all the great academic opportunities here at UCSD to capitalize on that.
Good luck - maybe I'll see you I'm 102C this quarter! :)