It's a lot like being a student. And working on your own often means that you lack a support group to lend assistance or a sympathetic ear to listen to your complaints. Clients won't call you back, companies won't answer your calls and email messages, and businesses will spurn the work that you spent so many hours on. All you can do is learn not to take rejection personally and be confident enough in your abilities to keep going. What's more, clients won't exactly rush to hire you if you have nothing to show them that demonstrates your brilliance.
Clients care a lot more about experience than education.
There are a couple of ways out of this dilemma. First, try to get some experience in your desired field while you're still in college. This can include work on college publications or productions, volunteer work at charities and intern work at local businesses or government offices. Don't even think about pay at this point. All you need is someone willing to give you a chance.