Compression on the nerves can cause this type of severe pain. As can a lot of trigger points that have built up over time. If you have both, it can be difficult and mystifying to track down. Find a good physio and get some treatment. With assessment they can help to determine if the disk compression on nerves is the issue. Or if compression on the trigger point recreates the pain pattern, you have trigger point stuff going on, instead or as well.
Groin combined with low back pain tends to be iliopsoas trigger points. Big general sweeping statement that may not be accurate. But may give you a place to start.
Here's a webpage at calmmindpainfreebody.com that gives some strategies on how to deal with: Hip Flexor (Iliopsoas) Pain Reduction Strategies
Good luck!
---------- Post added at 09:48 AM ---------- Previous post was at 09:45 AM ----------
And just to check, how old are you? Might your hip joints be causing you trouble? That can also cause severe groin pain, if they have degenerated.