I don't believe medics were officially allowed to arm themselves until the 60s (during Vietnam) for defense of their patients - and self-defense when their non-combatant status wasn't respected by the VC and NVA. However, this didn't stop individual medics from grabbing a .45 for the same reasons during WWII. Most brass looked the other way as it was understood that in the heat of combat medics often caught fire and the Japanese, as non-signators of the Geneva Convention, often targeted medics as they tried to tend to the wounded.
When I was in the 82nd Abn Division, our Division Chaplain, Jerry Autrey, was known as the "Gun-toting Chaplain" because as a young infantry chaplain in the 101st Abn Division in Vietnam he took up carrying an M-16 when in the field with the troops to make them feel more comfortable. If he was unarmed the guys felt as though they had to look out for him, with his own weapon (even if he didn't fire it) they felt he could take care of himself.
An interesting sidenote: during a combat operation things fell apart due to the op being commanded by a cherry lieutenant. Chaplain Autrey stepped in, organizing resistance, perimeter defense and calling in fire support. He received a Bronze Star for Valor for saving the 6s of the platoon, but a letter of reprimand from the 101st Division Chaplain on the same day for violating his non-combatant status. The guy was a legend among US paratroopers in my day.
I share this not only because I think it's a great story, but also it illustrates how the rules and reality often part ways in combat.