Sounds just like me, except my 10 days of antibiotics for bronchitis finished a few days before the bloody pee started. Bacteria didn't show up at first, so I think the UTI might have been caused by another problem. Antibiotics can cause stones, but I don't know how long they take to form. Definately tell your Dr. they can order scans and need to culture the urine to make sure you are on the right antiobiotic for that, probably different that the one your on for lung gunk.
First of all unlike males, in female anatomy, the reproductive organs are different and lying separately from the urinary organs. So fibroids have no relation with blood in urine unless or until there was any bladder trauma or the malignancy had spread locally.
Presence of blood in urine is called hematuria. Causes include lesions of the urinary tract, Kidney pathologies, trauma, tumors, malaria or stones in the urinary tract. In your case UTI needs to be probed thoroughly as to whether it is responsible for causing such symptoms.
I feel that without clinical examination, pinpointing a diagnosis is tough. Also a complete urine examination and culture may be required. Please consult a urologist for confirming the diagnosis.
I hope that helps. Kind regards.