Always had trace blood in urine. Had UTI 6 days ago follow up urine still has large amounts of blood. Blood work good no kidney pain. Bladder cancer?

Micro hematuria. Microhematuria in a 34 year-old female who has never smoked is not very likely to be due to bladder cancer. Bladder cancer is not really genetic in nature. Despite that, you should have a hematuria workup which would include imaging of your kidneys as well as a cystoscopy and a variety of possible urine studies.
Watch if it resolves. Uti an cause blood in the urine; this should clear up once the infection has been controlled which can take one to two weeks. Then get another urine test done. If the red cells(blood) in the urine persists then you should go see a urologist to make sure that your bladder is healthy and cancer free. It is unlikely that you have bladder cancer.