Hello and welcome to JustAnswer,
It sounds very much like you have a herniated lumbar dics.
This means that in your low back there may be part of a disc, a structure that sits between the vertebrae, that is pushing out and hitting a nerve. You would feel pain as you describe and it would be positional.
You need Xrays and an MRI if I am correct and there's not much else that can cause this kind of pain. HERE
is a helpful link to explain it in more detail.
You need to see your doctor as soon as you can, and, if you should lose control of your bowel or bladder function you should go directly to the ER as this is a surgical emergency.
As it stands and until you can see someone (and as long as you have no allergy to it) I would recommend taking motrin 600mg four times a day. You may safely add Tylenol too for extra relief.
The positional nature of your pain and the distribution of your pain suggests this diagnosis very strongly.
I am standing by if you have any questions, and by the way, a disc can herniate without any major trauma, a simple twist or bend can do it with discs that are weak from wear and tear over the years.