Do I need to get a college degree in order to be a freelance web developer

No you don't,. :)

No you don't but should you ever want to work for a company, some might require a degree of some sort. However, experience and a solid portfolio will always reflect better than a degree will on its own.

It also depends on what your potential clients are looking for. I've seen freelance positions that specifically want college students, and even one that wanted a copy of your transcript! Example: Student wanted to modify and enhance a Wordpress website for *****, a local environmental organization. Work will include improving SEO using WordPress plugins, fully implementing a 'donate' function, and expanding the website to be more than a blog. $15/hour. Must have enough experience to do the tasks listed with WordPress, without assistance. Completion of at least one WordPress class (preferably two) or equivalent experience is preferred. Interested students should send a list of WordPress-related classes completed and grades received in each (or unofficial transcript) plus links to examples of work.

Most freelance positions don't require a degree or to prove that you're a college student. That being said you need to have a solid understanding of the languages you want to freelance in and some small business knowledge as well, like knowledge of the local market. Unlike something that requires certification, registration, or licensure like a therapist, a lawyer, a nutritionist, a nurse, etc. there are no standards for someone to work in IT freelance. The people that set the standards are the people that you choose to have as clients. So you don't need to "prove" with a degree that you know what you're doing, you'll need to prove to your clients that you know what you're doing through your skills and your ability to get their projects in during the timeframe that you both agree upon.