Some discomfort and a few drops of blood after first intercourse is common and comes from small superficial tears at the vaginal opening, which heal on their own within a few days. Burning while passing urine afterwards is also common, because urine passing over those small abrasions stings. That is different from a urinary infection, which usually builds over a day or two with frequency and urgency.
Next Steps
Drink plenty of water, keep the area clean and dry, and avoid intercourse until you are comfortable. Because this was without a condom, take a urine
pregnancy test if your period is more than a week late, and consider a contraception discussion with a gynaecologist.
Health Tips
Bleeding that is heavy or continues beyond a couple of days, worsening pain, fever or a foul discharge should be examined rather than waited out.