Go through one of the popular algorithms books first. There are a few recommended ones. Some are better for self study than others. If you just need an algorithms course, no sense wasting 4 years on it.
Agreed, you don't need to pursue a degree to pass these interviews. You can learn all you need to know about time complexity in probably a few hours, then it's just practice/pattern matching.
That sounds like a good place to start. And probably better than committing a bunch of time and money right off the bat. Maybe I should get through one of those first and then consider another degree if I still feel like I need more.