Hello, Welcome to Just Answer and thanks for your question. The type of pain you are having is typical of nerve compression at L3/L4 and possibly at L4/L5. Check out the dermatome map in this link: http://www.backpain-guide.com/Chapter_Fig_folders/Ch06_Path_Folder/4Radiculopathy.html
As spinal nerves exit on each side of the body, they may be compressed, causing pain downstream from that nerve. You can see on the map where pain may be caused from a compression at L3/L4 versus L4/L5 (and of course, it could be a compression at both places). You may have more compression on one side than you do on the other, meaning more pain in the right leg than in the left.
A neurosurgeon is definitely the referral you need. I am happy you are getting a quick appointment. In the meanwhile, you should take your pain medication (Zipsor/diclofenac) on a regular schedule. It is best to take it regularly than to wait until the pain is unbearable. Be sure to eat something when you do take it since it can irritate your stomach. If it is not controlling the pain, you may need a narcotic in addition to the anti-inflammatory medication. Another thing they might want to try is steroid injections. Sometimes that can provide relief for 1-3 months. While you are waiting for your appointment, you should consider using an assistive device like a cane or walker. A problem of this kind means that your leg may suddenly fail to support you and you could have a nasty fall, and that could injure your back or limbs even more.