Hello,
Thank you for your query at DoctorSpring.com
I understand your concern.
With such a small area of burn, you should not worry. Make sure the area is clean. You can wait till morning to see the doctor. If you have an ointment like Soframycin or any silver sulphadiazine ointment, you can apply it on the burn wound.
Feel free to discuss further,
Regards.