Do utis make it painful for me to ejaculate, urinate, or both?

Painful urination. Urination can certainly be painful with utis, ejaculation can be painful if you have prostatitis +/or inflammation of prostatic (upper) urethra as part of your uti.
Both. Having a urinary tract usually causes urinary symptoms but not always. It is usually painful or causes discomfort with urination. It can also affect the prostate and depending on the severity may cause some discomfort with ejaculation. With some prostate infections, there may also be blood seen in the semen but this usually resolves over time with adequate treatment.