Ethical question regarding treating a dying patient’s pain

I experienced a distressing situation and would like to get input from physicians.

My patient was in severe septic shock but alert and following commands. The patient was complaining of severe pain in their hips and we were unsure what the source of the pain was. The patient was very restless and appeared to be in great distress.

SBP was in the 60's-70's so Levophed was started. After achieving a MAP of >65, Fentanyl was given but was not helping. We strongly suspected the patient was going to die and they did.

What bothers me is the fact that the patient lingered in pain for hours, unable to get adequate analgesia d/t their hemodynamic instability. I asked if we were going to intubate (we did not), thinking at least the patient could be out of pain while we did everything to treat the sepsis.

How do you make a patient comfortable (who is a Full Code) who is hemodynamically unstable and actively, painfully dying? Is there justification to put this person into a medically-induced coma? An ethical obligation?