It would be very unusual for a fall to cause lumbar lordosis directly but i think it could easily develope afterwoods because of the trauma to the spine

Yes. Very common. It probably knocked out your other SIJ or both (ilium upslip) and that is why you got lordosis. You should find someone to push it/them back to correct place.

There is no scientific evidence that back pain is affected by increased or decreased lordosis.

Your pain is probably from a sprain or facet jamming.

Does it hurt worse to bend forward or lean backward?

Buttermere

There is scientific evidence that depression pills are useless for most people and lowering your blood colesterol with pills cause cancer and other problems. Still billions of people use them.

Decreased lordosis is not a direct cause of pain. It is just one symptom caused by malaingned joints. Pain comes later, sometimes after decades when muscles get tired of supporting poor posture.

I've had exaggerated lumbar lordosis since I was a child. By the time I was a teenager, it started getting painful at times, due to the muscles and tendons growing and shifting to better protect the spine. Or so I was told by my G.P.
I'm now in my thirties, and had a pretty bad car accident a few years ago. Because of the extra trauma, I've started experiencing chronic pain. I was off work for a few years, being unable to stand or walk for more than 20-30 minutes at a time. I was put on slow release percocet to manage the pain, and am now back to work full time, and enjoying nightly walks with my husband.
Lordosis was NOT the main cause of my chronic back pain. The pain was a culmination of the lordosis, the severe whiplash, and the past trauma of trying to ease the discomfort myself .

If you never had lordosis its possible that you would not have any problems with your spine. lordodis can be the initial condition that leads to many types of different spine pathology, people with chronic back pain often have a long history of worsening back conditions with lordosis being one of the initial conditions that was present at the beginning of the patients complaint. It may not be the cause of the pain from a problem such as a herniated disc but it could have been the cause of a degenerative process that lead to the herniated disc in the first place.