It is unlikely. The ultrasound machine produces sound waves, not heat. You should only feel the transducer head rubbing on your skin. If you felt the burning sensation as soon as the transducer head was put on your body, it is possible that it was already heated up from an earlier session on another patient.
It is common to feel warmth during therapeutic ultrasound. The sound waves can be turned into heat energy in the tissues of your body. The heat energy then travels to the skin surface, where the heat receptors are located. If the temperature in the tissues ever got too hot, you might feel a painful burning sensation. Your tissues are not actually being burned, but you still need to let your therapist know. This kind of pain isn’t appropriate for ultrasound therapy. That is why therapists don’t do ultrasound treatments in areas that have a loss of sensation for some reason.