It's more common than you would think. We get a lot of people who describe a continuous, sometimes debilitating dizziness/lightheadedness. Here's a few links to threads from people in similar situations (the threads are a bit old, but they contain a lot of valuable info I think you'll relate to):
http://www.medhelp.org/posts/Anxiety/24-7-dizziness-/show/4545
http://www.medhelp.org/posts/Anxiety/always-feel-lightheaded-and-dizzy/show/514577
It sure sounds like anxiety IMO as well, and here's why....for one, you're young, and the likelihood of you having something very seriously wrong (like a brain tumor, etc) is slim, not to mention, you've been thoroughly evaluated by many different specialists, more than once. If there was something big and bad going on, one of the doctors would have most likely found something abnormal in the findings of your diagnostic tests. Lastly, to me, it's telling that the Klonopin DID help you to an extent. Most likely, if you were on a more therapeutic dose (and dosing schedule), you would notice a lot more relief. Klonopin is a medication that is most effective when dosed at least twice a day. It's a longer term benzodiazepine that builds in the blood plasma to allow for a more steady state of calm, whereas the shorter acting benzos, like Xanax and Ativan, are better served as rescue meds, to be used when anxiety is very high (ie poanic attack).
Like Lron says, if indeed the dizziness is caused by anxiety, the best thing you can do is to try NOT to focus on it, think about it, and definitely quit searching the internet about it (Dr. Google is a HUGE trigger for anxious folks...especially when it comes to health related anxiety). It's easier said than done, yes, and it takes time, and usually the help of a good therapist, who can help you learn how to manage those anxious thoughts...redirect the brain when those "what if" thoughts start spinning around. Medication may also be a valuable tool for you, along with the therapy. There are many different antidepressants commonly prescribed to help manage symptoms of anxiety. Good starting places would be Zoloft, Lexapro.
So, a good next step would be to ask your doctor to a referral to a psychiatrist, who can discuss medications with you (if you're interested in trying that), and a therapy referral to get that ball rolling. It's preferable to find a therapist who is well versed in CBT (cognitive behavioral therapy) if possible. CBT is a slightly different therapeutic approach compared to the more traditional talk therapy. CBT helps you to learn new ways to think, react and cope.
I know it's frustrating to experience such REAL physical symptoms and try to accept that anxiety could be the cause. So many people really struggle with the acceptance part of things....and they continue chasing their tail, trying to find that elusive medical diagnosis that is causing their symptoms. Sadly, this only keeps the person "stuck". By all means, continue working with your doctor(s), but starting to address the anxiety is reasonable...because even IF anxiety isn't the underlying CAUSE for your symptoms, it's certainly a factor now.
Best to you, keep us posted!