22 F, urine culture came back as negative and doctor is refusing to prescribe me anything for UTI pain. What are my options? What could this be?

Another diagnosis. Painful urination with negative urine culture suggests a diagnosis other than A bladder infection. Conditions to consider are inflammation of the genital area, STD's and interstitial cystitis. Suggest you talk to your doctor about conditions other than UTI that might be causing your symptoms.
Need to evaluate. You did not describe your symptoms. Since you do not have UTI the cause of pain needs to be determined and that can only be done by in-person evaluation. You may seek a different doctor. In the mean time you may take over the counter pain relief.