Could a bone marrow biopsy in the left hip leave you will hip pain or problems after?

No: it is done in tue pelvis, not the hip.

Yes: Might a bone marrow biopsy, which occurs in region of the posterior iliac crest, cause chronic pain in this region; which many lay people term the "hip"? Chronic pain is uncommon & suggests ilio-lumbar ligament injury & associated sacroiliac joint instability. The same chronic injury occurs when Orthopedists ignorantly harvest iliac crest bone during vertebral spine fusion operations.