Pain running down the leg in most of the cases is due to entrapment of nerve in the lumbar spine i.e prolapsed disc pressing the nerve exiting at that level.
Unable to stand and walk features are more common in cases with lumbar canal stenosis but it presents mostly in elderly patients with severe osteophyte at the margins.
In your case because of weight central disc bulge may be causing features like canal stenosis. An MRI showing lumbar canal diameter at different levels will exactly reveal the picture.
Straightening of lumbar vertebrae is due to protective spasm as body itself tries to prevent any further damage.
Next Steps
See a knowledgeable physiotherapist who can guide you with proper exercise and design a proper physio treatment protocol which will include electrotherapy and manual techniques.
Health Tips
1/ Avoid postures that aggravate the symptoms.
2/ Be more often in postures that reliefs the symptoms.
3/ Avoid complete rest as it makes the case worse later on. Initial few days, one can be on complete rest. Change posture every 20 mins.
4/ Avoid lifting/ bending forward.
5/ If weakness in leg like difficulty in lifting the foot immediately see a good orthopedic surgeon.