You definitely can learn to code without going to a major university. If I understand this right, you do some kind of online college? (Sorry I’m not that experienced with colleges since this is a little bit different here in Austria)
To answer your question: Yes. If you have the time and the motivation to dive deeper into web development before you get there in class, you should definitely do it. It might help you in your course later on if you already have some experience in that field.
There are some kind of modules for Frontend and Backend development. If you manage to finish all tasks and challenges, you can even get a certificate for each of the modules.
If you get far enough, you can even participate on real projects for non profit organizations, so you can practice what you’ve learned on real tasks.
What I really like there is, that most of the learning tasks are small enough to make some progress, so it might fit into your schedule.
I hope I could help you, good luck with the studies :)