A pinched nerve can indeed be quite painful. When a nerve becomes pinched where it leaves the spinal cord, it can cause pain in the distribution of the nerve itself, similar to what you describe. However, the location of the lower back and into the groin and hip is not as typical for a pinched nerve and instead suggests several other different possibilities. A process intrinsic to the hip itself, including arthritis
or joint impingement, can refer pain to the groin and the lower back. In addition, kidney stones
or other kidney issues can also start with pain in the lower back and then wrap around to the groin area. In men, testicular pain can radiate up to the groin, while in women ovarian pain can refer to the lower back and then to the groin.
In general, there are many different reasons for the pain you describe, and the best way to sort it all out is for you to see your primary care physician
right away. He or she will want to get many additional details about your pain (when/where it started, where it is now, if anything helps or makes it worse) as well as any additional symptoms you may have noted that may suggest a possible explanation. A physical exam will also be important to see the pain can be localized and if any additional imaging tests might be needed. Hopefully you'll be feeling much better soon, but since your symptoms could represent man things, it is important to see a physician right away.