Welcome to HCM.
You can continue your birth control pill but also take missed pill with regular pill if it is within 24 hr.
You have to start proper antibiotic complete course for urinary tract infection
immediately.Take oral pill and antibiotic at different time.
Red color urine is usually due to some blood in the urine suggest severe urinary tract infection.Confirm urinary tact infection by urine routine/micro investigation also rule out any stone formation by USG abdomen.
Drink more liquids and water.
Take proper local care.