Web programming is a bit different from CS, especially HTML/CSS/JS etc. It’s in the space of CS, but especially academically, it’s not the focus at all. It sounds like the closest thing to what you’re doing is web programming, though I don’t think many offer it as a degree. Many websites use heavier CS languages now, but web design / front end design specialist type person is still significantly common. Most schools, in their entire CS department, have a course or a few courses on the subject, usually later electives. CS theory and logical math WILL be a significant portion of academics for a CS degree.
For web programming v CS, which do you actually prefer? Websites and their design aesthetically or complex / efficient / detailed programs? That question should help you in direction there. Consider hte first end design, the other end CS, and the middle a mix aka web programming.
Design and Game Programming aren’t as linked as many people think: a good game programmer will need to essentially have a CS background PLUS the artistic eye. Essentially it’s a dual degree. Otherwise, you will be in one subspace: a straight CS major can work with gaming, or a designer can aid and design game graphics without the full CS ability.
As far as straight design, that’s a fair option. Don’t write it off. Personally, I think it sounds like the most likely option from the OP.
It sounds like Psych is a personal interest: good. Take a few classes and maybe a minor, but I would recommend against a double major. Enjoy it, learn, but it sounds like its a god secondary option.
You’re a junior, there’s no need to decide QUITE yet.
For your college search, I recommend looking for design schools, and then one of schools that offer web programming / some variation that isn’t straight CS and/or straight CS schools, depending on the answer to the above. Then pick between the tow/three later in the process as you think on the options.
One note: I also came from design and web programming: I started in photoshop, picked up HTML/CSS my sophomore year, then progressed to C, PHP, and eventually on to AP CS. I’m now a CS major and couldn’t be happier to leave to straight web programming behind. I can do it, but I would much rather work on the complex details, algorithms, large systems, and other classical CS topics.
Good luck! You seem to be thinking about all the right things, you’re in a good position.