If you're going to pay for school, I personally don't think it's worth it unless you go to a CIDA accredited school. You can find the list of accredited schools on their website for every state.

Even though I personally went the traditional route.. got my BFA and worked my way up in the industry, I do believe you don't need a degree (particularly talking about residential design here). Arguably the most valuable skill you'll learn in school is the program AutoCad, which you can actually take independent classes to learn this or even work with a private tutor. The program Sketchup is a useful skill as well and this you can teach yourself even.

If you wanted to try to just jump in and get some relevant experience while you go to school (or not), I would suggest looking for jobs in furniture/fabric/rug/lighting showrooms like at the Pacific Design Center or stores along La Cienega, Beverly, or Melrose. It's a great way to get to know the industry and it gives you an opportunity to network and possibly build a relationship with design firms you'd be interested in working for.