sounds like asacroiliac joint problem...
describe the quality of the pain in your hip and the pain in ur back each...e.g dull, unspecific,or sharp, specific, can you place ur finger on the spot where the pain is in ur hip and your back?
does the pain in ur hip happen at the same time with the pain in your back?
My theory is...you probably have a sacroiliac joint that is more predisposed into an anterior pelivc tilt (perhaps owing to a surgery that has left your hamstings weak, making the thigh muscles-rectus femoris more dominant, during a squat you need controlled concentric and eccentric contol of hamstring and quads, this balance seem affected hence your knee not able to support you weight). each time you do a heavy squat that anterior pelvic tilt is emphasized and strains, the posterior ligament of theSIJ. If the answer to the above questions are that the pain feels unspecific in ur hip and your back and that the hip and back pain occur together or that the pain on the side of the dimple of your back happens at the same time with those other patterns of pain, then this may mean a referral pain in the hip and back...
this would explain why rolling your hip backward (taking it into posterior pelivic tilt) relieves it...with rowing (depending on what angle you are sitting) the might be small alternations between anterior and posterior pelvic tilts putting some strain on these ligaments...overuse for lack of a better term...
The other theory still relates to the predisposition of a pelvic tilt anteriorly with compression of your hip flexions as they compress and elongate during flexion and extension of squatting.
Either way...you need to see a physio wherein the following can be assessed
Your lumbar spine (to rule out this as a cause)
To examine your hip to see if this is due to a joint pathology (unlikely due to your age)
your sacroiliac joint to see how the lumbopelvic biomechanics work in comparison to the other side and to see if any provocation tests/palpation will reproduce this pain you have
the length/tension discrepancy between your hamstrings and your quads..also your back and belly muscles
your general posture to see where this alignments fit in with the theory
I dont know if I have been of help or made things too complicated...but thats the hypothesis I would work on based on what you've posted
cheers