I would consider myself someone who believes in divine healing and has seen it occur from time to time when sharing the gospel message.
One of the biggest barriers to hospital ministry is the structures set around it. I have attempted to ask hospitals to allow a table for people to come to for prayer. I have also attempted to create small fridge magnets, with a QR code to a prayer website, and attempted to put them in hospitals. In all of these circumstances, the answer from the hospital has been "no", or sheer silence.
Then, for me, there is a fear barrier, it is hard to act in faith when you know the hospitals don't want you there, and you are uncertain how people will respond also. I know this because I was admitted to the hospital recently, and had opportunities to pray, but fear prevented me.
I know it is a little cowardly, but when I was in emergency, I prayed for the people there without them knowing, that God would take away their pain, and illnesses, as they sat in the emergency department. Whether or not some of those prayers were answered I will never know, but one man who was admitted in terrible pain for a suspected broken leg was admitted at the same time as me. I prayed for him as I sat there, by the end of the night, he had no pain, he had his scan, and it was found his leg was not broken, the doctor could only put his initial pain down to a possible back spasm. Like I say I don't know if it was the prayer that helped him, but he was good to go home.