D9110 is for an emergency palliative treatment. D0140 is to exam a problem focused area.
Usually D9110 is for a same day emergency appt and you may only exam, take an X-ray, prescribe Rx or an open and drain to alleviate immediate pain. If this was an appt set up a week or days in advance then it was most likely a problem focused exam. 9110 is only payable in the scenario where you have not rendered any treatment but you have triage the patient to alleviate any pain your narrative should include that you performed an exam took an x-ray and prescribed any RX.
Also provide the tooth number
Some plans share frequency with the exams codes so be sure to confirm benefits and frequencies to properly treatment plan your patients cost.

correct codes for this appointment D0140 and D0220

D0140 and D0220 are the correct codes. You only bill for D9110 when a patient initiates an appointment because they are in pain and you then do a minor procedure to alleviate the patient's pain. For example, smoothing a tooth down, applying fluoride varnish to a single tooth for sensitivity, or anesthetic applied to relieve pain.

You can bill for D0140 and any x-rays taken along with D9110. You many need to put a narrative and some insurances require chart notes for D9110. The main thing to remember it to only bill for D9110 when the patient has initiated the appointment because they are in pain or discomfort and you have completed a minor procedure to relieve that pain.