Since I have three chipped discs in my lower back, I am familar with lower back pain. In fact, I blew out my lower back last Tuesday while simply standing up. I have to take special care of my lower back because of my situation, and have been seeing a chiropractor for close to 15 years. He adjusted me three times last week after my lower back kicked out, and I credit those adjustments with getting me back on my feet and almost back to normal. I am still stiff and sore, but can actually walk upright without any pain. Going from sitting to standing is still a little tender, but it's getting SOOOO much better.
With that said, I wouldn't let a regular/medical doctor go near my back if I were you. They are not trained as a chiropractor is in the care of the spinal column. Medical doctors think in terms of medicine and surgery, neither of which you need. You need your spine aligned so that your muscles will quit spasming, disabling you from walking upright, as you said.
This brings me to my next point. You said you weren't sure whether your problem was muscular or skeletal. It is likely BOTH. When a vertebrae pops out of alignment (which can happen very easily under the right circumstances), the muscles will spasm. They are attached to the bone, and just the slightest movement on the bone's part will pull the muscles, causing them to spasm. This is usually the source of the pain because the spasms can be quite violent. The ones I had last week literally knocked me over! I'd drop straight to the floor. It also sounds like you have a pinched nerve, being that you said you can feel it down your leg. This is bad. If a nerve is pinched for a prolonged time, the nerve endings for that pinched nerve will eventually die, which will lead to your muscles not responding to signals from the brain. I know a guy whose nerve endings to his feet died due to a pinched nerve in his spinal column. He has to lift his leg really high and then flop his foot down when he walks because he can't move his foot. Moreover, when a vertebrae misaligns, the rest of the spinal column (and thus, the rest of the bones in your body) will attempt to adjust and compensate for the misalignment. This usually leads to a curvature of the spine (most people have slight curvatures in their spine - I have one - as a result of the spine naturally re-adjusting), and other skeletal problems (loss of normal curves in the spine, hips rotating front to back, one leg being longer than the other and causing knee pain in the shorter leg, one shoulder appearing "higher" than the other, your head tending to fall to one side, etc.).
If you had disc problems in your lower back before, I would highly encourage you to see a chiropractor REGULARLY! I go to mine at least once a month. I remember being in so much pain before I started seeing a "bone doctor". I couldn't even climb a flight of stairs without excruciating leg pain. Now, I can run up and down stairs, lift weights, walk long distances, have reduced headaches, and feel so much better. Yes, I occasionally get the lower-back blowout (as I had last week), but the recovery is so much easier and faster with chiropractic.
Oh, and I wouldn't recommend exercising until you get this taken care of. You'll only worsen it. Ask your chiropractor to give you a series of good stretches and strength exercises to strengthen your lower back once you're better. I have to modify many of Cathe's core exercises because they aren't always the best for people with lower back problems. If your chiropractor can't give you these exercises, find a different chiropractor (not all chiro's are alike - I went through a few before I found the one I have now, and he's a back-healing SUPERSTAR)!
