Funnily enough I had this about a month ago for the first time. It was mainly around the base of the middle finger just on the palm as you say, but my middle and ring fingers were aching in a weird way around the joints when pressed in certain directions. I could still climb and there didn't seem to be any lack of strength etc., but it just hurt.
It felt like there was 'lump' on the tendon when I pressed at the bit as the finger joins the palm. I massaged it really heavily, strectched it out, put NSAID gel on it (probably didn't do anything but who knows?) and took it easy on fingery climbing for a couple of weeks. Seems all OK now and has done for a week or 2. As it started to get better the painful area seemed to 'shift' across to under the pinky finger, no idea what that was about.
Still don't really know what it was or what caused, but it didn't seem major in the end. The closest thing I could find to the symptons when looking online was early stages of trigger finger, but not sure if that's what it was?
